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C L A S S E S

Chapter - 17

(Thermal Properties of Matter)

1

Raja Sir Income Tax Inspector

14 Years’ teaching experience

•CAT •GMAT •UPSC •SSC •BANK

THERMAL PROPERTIES OF MATTER Heat

Heat is a form of energy, which produces the sensation of warmth. It is responsible for the change in thermal condition of the body.

Its SI unit is 'joule' and cgs unit is ' calorie' which is also, widely used. When a body gets heated, various types of change occurs such

as expansion, contraction, change of state, change of electrical properties, etc. The heat energy that is transferred from one body to

another, can change into mechanical energy, electrical energy, etc.

Temperature

Temperature is a quantity, that expresses the degree of hotness or coldness of a body. The flow of heat from one body to another

body is due to their temperature difference, e.g., if on dropping a very hot spoon in water container, containing cool water, heat

flows from spoon to the water. So, it is clear that temperature and heat are different things. It is measured in several arbitrary

scale: like Celcius, Fahrenheit, Kelvin, Reaumur.

Measurement of Temperature

The device which measures the temperature of the body is called thermometer. It was developed by Galileo, who found that the

gases expand on heating. As temperature is a variable quantity in different conditions. Therefore, different scales are provided to

measure it.

Temperature Scales

To measure temperature, two fixed points are taken. One of them is the freezing point of water, known as ice point and other fixed

point is boiling point of water, known as steam point.

Some temperature scales are as follows

Celsius Scale (°C)

In this scale, temperature is fixed from 0 (zero). Scale is divided into 100 equal parts called degrees. Ice point and steam point are

taken as 0°C and 100°C. This scale was designed by Anders Celsius in 1710.

Fahrenheit Scale (°F)

In this scale, ice point and steam point are taken as 32° F and 212° F respectively. This scale is divided into 180 equal parts. It was

designed by Gabriel Fahrenheit in 1717.

Kelvin Scale (K)

In this scale, ice point and steam point are taken as 273 K and 373 K, respectively. This scale is divided into 100 equal parts. It was

introduced by Kelvin in 1724.

2

Manisha Bansal Ma'am (Director & Author)


•CAT •GMAT •GRE •SSC •BANK

3




Reaumur Scale (R)

In this scale, ice point and steam point are taken as 0 R and 80 R. This scale was introduced by RA Reaumur in 1730.

Rankine Scale (Ra)

In this scale, ice point and steam point are taken as 460 Ra and 672 Ra. It was introduced by JM Ranking in 1859.

Relations between various temperature scales are as follow

C F 32 R K 273 Ra 460

100 180 80 100 212

Transmission of Heat

Transfer of heat from one place to other place is called transmission of heat. There are three processes by which transmission of

heat takes place.

1. Conduction

It is the process of transmission of heat, in which heat goes from one particle to another

particle of substance but no particle leaves its position. In solids, transmission of heat takes

place by conduction process.

In metals, thermal conduction is due to vibration of atoms and free electrons.

2. Convection

It is the process of transmission of heat, in which particles of substance goes to

another place after taking heat from the source and other particles come to their

place. In liquids and gases, transmission of heat takes place by convection process.

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Principle of chimney used in the kitchen or a factory is based on convection land and sea

breezes are due to the convection.

3. Radiation

It is the process of transmission of heat, in which there is no need of medium for

transfer of heat. It is the quickest way of transmission of heat. Heat from the sun comes

to the earth by radiation. Dark colored objects absorb radiation better than the light-

colored object.

Transformation of Phase

When matter changes from one state to another it is called a phase transition.

Various processes involved in this are:

• Gas to solid phase transitions are known as "deposition."

• Gas to liquid phase transitions are known as "condensation."

• Liquid to gas phase transitions are known as "vaporization."

• Liquid to solid phase transitions are known as "freezing."

• Solid to liquid phase transitions are known as "melting."

• Solid to gas phase transitions are known as "sublimation."

• Gas to plasma phase transition is known as Ionization

• Plasma to gasphase transition is known as Recombination.

Dry Ice - Solid carbon dioxide is known as "dry ice" and sublimates at room temperature.

Plasma is the fourth state of matter which does not have a fixed shape or volume and are less

dense than solids and liquids but unlike ordinary gases, they are made up of atoms in which few or

all the electrons have been stripped out and the ions move freely.

Triple point:

The triple point of a substance is the temperature and pressure at which the three phases of that substance(Solid, liquid and gas)

exist together in thermodynamic equilibrium.

Or It is that temperature and pressure at which the sublimation curve, fusion curve and the vaporization curve meet.

Triple point of water is 0.01 C

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There are many combinations of Pressure and Temperature where substancecoexist as (solid – liquid), or (liquid – gas) or (gas –

solid) phases.But there is only one combination of pressure and temperature at which the three phases can coexist as (solid, liquid

and gas phase), i.e.AT TRIPLE POINT

But there is a particular pressure and temperature combination or particular point in which increasing either pressure or

temperature or both, the substance cannot be distinguished whether it is a liquid or gas.The phase is called super critical fluid. This

point is called critical point of that substance.

s-v line where both solid and liquid form exists together

s-l line where both solid and vapour form exists together

l-v line where both liquid and vapour form exists together

Variation of melting & Boiling points with Temperature

Melting pointand boiling point varies with Temperature

Since our surroundings has Pressure= 1 atm. So, we consider value of Temperatureat 1 atm

boiling point = 100°C at 1 atm

Melting point= 0°C at 1 atm

Specific Heat

The amount of heat required to raise the temperature of 1 g of a substance by 1°C is called the specific heat of gas.

It is represented by s. Its unit is cal/g°C or joule/g°C.

s = Q

m t

where,

Q = amount of heat given to the substance

m = mass of the substance

Δt = rise in temperature

There are two types of specific heat of gases

1. Specific Heat at constant volume (cv)

At constant volume, the amount of heat required to raise the temperature of 1 g of a gas by 1°C is called specific heat at constant

volume (CV). Its unit is cal/g°C.

2. Specific Heat at Constant Pressure (cp)

At constant pressure, the amount of heat required to raise the temperature of 1 g of a gas by 1°C is called specific heat at constant

pressure (CP). Its unit is cal/g°C.

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Latent Heat

At constant temperature, the amount of heat taken by 1 g of a substance to change its state is called latent heat of substance. It is

represented by L, its unit is cal/g.

Latent heat of vaporization is inversely proportional to the temperature and is maximum at 0°C. Variation of latent heat of water

vapor with temperature is negative.

heat, Q = m(mass)× L(Specific latent heat) it happens at constant temperature

100

Ice Water

& Ice

Water all

liquid

Water

and Steam

(Steam)

Water

Vapour Mct

Latent Heat

0° C

Mct

Mct

Latent Heat

0

–20

–40°C 0 20 100 200 740

Heat added (k cal)

Calorific Value:

The amount of heat obtained by 1 g of a fuel is known as its calorific value. Out of all the substances, hydrogen has maximum

calorific value.

Note:If a pendulum designed at certain temperature is allowed to move/work at different temp. Then time difference is observed or

correct time is not shown.

Time is lost or gained by pendulum per second.

Calorimetry

It is the science of measuring the changes in the state variables of a body due to transfer of

heat in order to calculate the effect of heat transfer on obtained changes. This is performed

using Calorimeter.

Principle of Calorimeter

When two bodies of different temperature are kept in contact, then flow of heat between

them takes place from the body at higher temperature to the body at lower temperature. This

flow continues till both the bodies attain the same temperature.

Car Engine Coolant

Water is used as a cooling liquid in car engine because its specific heat capacity is high and

water absorbs more heat for each degree rise of its temperature. However, water alone is not

sufficient for cooling a car engine. One needs to add a coolant such as ethylene glycol,

potassium dichromate, tri-sodium phosphate, and sodium nitrate.

Entropy

It is the degree of order or randomness in thesystem and is thermodynamic function which depends only on the temperature of

system only.

Entropy (𝛿S) = Heat absorbed( Q)

Absolutetemperature(T)

𝛿Q = T𝛿S

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Entropy of a substance is zero at absolute zero temperature. Water at 0°C is assumed to have zero entropy, and changes in its

entropy are reckoned from this temperature.

Cooling at the night

The earth and other objects on it, receive solar radiation during the day and become

warm. But at night they start emitting radiant energy and become cool. Cloudy nights are

warmer than clear nights, because clouds reflect the radiations emitted by the earth at

night and keep it warm. Thus, clouds acts like a blanket.

Greenhouse effect

The radiation from the sun when reaches to the earth surface is of shorter wavelength,

some part of it is absorbed by the earth surface and some part is reflected back. The

reflected radiation is of larger wavelength So, it is trapped by the layer CO2 molecules

present in the atmosphere.So, the trapped radiations are reflected back towards the earth surface, thereby rising the temperature

of entire earth. This effect is known as Green house effect and the CO2 is known as Green house gas.

Newton's law of cooling

If a body is at higher temperature then surrounding than it looses heat to the surroundings

The rate of cooling of a body is directly proportional to the temperature difference of body and its surroundings.

e.g. hot water takes much less time in cooling from 100°C to 95°C than from 20°C to 15°C. If hot water and fresh tap water are kept

in a refrigerator, the rate of cooling of hot water will be faster than the tap water.

Mathematically, – 0

dQ(T T )

dt ⇒ Rate of heat loss, 0

dQk(T T )

dt

⇒

dms

dt

= k ( – surroundings)

Black body

A perfectly black body is one, which absorbs completely all the radiations of whatever wavelength is incident upon it. Since, it

neither reflect nor transmit any radiation, it appears black whatever the colour of the incident radiation may be.

Emissive Power (e)

It is defined as the amount of heat radiated by unit area of the surface in one second at a given temperature and for given

wavelengths. Its unit is J/m2 second.

Absorptive Power (a)

It is defined as the ratio of absorbed radiation to the total incident radiation. It has no unit.

The silvered surface of a thermo flask is a bad absorber. It does not absorb much heat from the surroundings. That is why ice inside the

flask does not melt. Also, the silver surface is a bad emitter/radiator, therefore hot liquids inside the flask do not cool quickly.

9




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KINETIC THEORY OF GASES The kinetic theory of gases describes a gas as a large number ofsubmicroscopic particles (atoms or molecules), all of which are in

constant, rapid, random motion. The randomness arises from the particles' many collisions with each other and with the walls of

the container.

Kinetic theory of gases explains the macroscopic properties of gases, such as pressure, temperature, viscosity, thermal

conductivity, and volume, by considering their molecular composition and motion. The theory posits that gas pressure results from

particles' collisions with the walls of a container at different velocities.

Assumptions of kinetic theory of gases

1. Every gas of extremely small particles known as molecules. The molecules of a given gas are all identical but are different from

those of another gas.

2. The molecules of a gas are identical spherical, rigid and perfectly elastic point masses.

3. The molecular size is negligible in comparison to intermolecular distance (10-9 m).

4. The speed of gas molecules lies between zero and infinity very high speed.

5. The distance covered by the molecules between two successive collisions is known as free path and mean of all free paths is known

as mean free path.

6. The number of collision per unit volume in a gas remains constant.

7. No attractive or repulsive force acts between gas molecules.

8. Gravitational forces on the molecules is ineffective due to small masses and very high speed of molecules.

Kinetic Theory of Matter

(a) Solids:It is the type of matter which has got fixed shape and volume. The force of attraction between any two molecules of a solid is

very large.

(b) Liquids:It is the type of matter which has got fixed volume but no fixed shape. Force of attraction between any two molecules is not

that large as in case of solids.

(c) Gases:It is the type of matter does not have any fixed shape or any fixed volume.

• Ideal Gas:A ideal gas is one which has a zero size of molecule and zero force of interaction between its molecules.

• Ideal Gas Equation:A relation between the pressure, volume and temperature of an ideal gas is called ideal gas equation.

PV/T = Constant or PV = nRT

Here, n is the number of moles and R is the universal gas constant

Real Gas:The gases which show deviation from the ideal gas behavior are called real gas.

• Vander wall’s equation of state for a real gas:

[P+(na/V)2][V-nb] = nRT

Here n is the number of moles of gas.

a and b are van der waals’ constants.

Avogadro’s number (N):Avogadro’s number (N), is the number of carbon atoms contained in 12 gram of carbon-12.

N = 6.023×1023

(a)To calculate the mass of an atom/molecule:

Mass of one atom = atomic weight (in gram)/N

Mass of one molecule = molecular weight (in gram)/N

(b)To calculate the number of atoms/molecules in a certain amount of substance:

Number of atoms in m gram = (N/atomic weight)×m

Number of molecules in m gram = (N/molecular weight)×m

(c)Size of an atom:

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Volume of the atom, V = (4/3)πr3

Mass of the atom, m = A/N

Here, A is the atomic weight and N is the Avogadro’s number.

Radius, r =[3A/4πNρ]1/3

Here ρ is the density.

Gas laws

(a) Boyle’s law:It states that the volume of a given amount of gas varies inversely as its pressure, provided its temperature is kept

constant.

PV = Constant

(b) Charler's law or GayLussac’s law:It states that volume of a given mass of a gas varies directly as its absolute temperature,

provided its pressure is kept constant.

V/T= Constant

V–V0/V0t = 1/273 = γp

Here γp (=1/273) is called volume coefficient of gas at constant pressure.

Volume coefficient of a gas, at constant pressure, is defined as the change in volume per unit volume per degree centigrade rise of

temperature.

(c) Gay Lussac’s law of pressure: It states that pressure of a given mass of a gas varies directly as its absolute temperature provided

the volume of the gas is kept constant.

P/T = P0/T0 or P – P0/P0t = 1/273 = γp

Here γp (=1/273) is called pressure coefficient of the gas at constant volume.

Pressure coefficient of a gas, at constant volume, is defined as the change in pressure per unit pressure per degree centigrade rise

of temperature.

(d) Dalton’s law of partial pressures: Partial pressure of a gas or of saturated vapors is the pressure which it would exert if

contained alone in the entire confined given space.

P= p1+p2+p3+……..

nRT/V = p1+p2+p3+……..

(e) Grahm’s law of diffusion: Grahm’s law of diffusion states thatthe rate of diffusion of gases varies inversely as the square root of

the density of gases.

R∝1/√ρor R1/R2 =√ρ2/ ρ1

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So, a lighter gas gets diffused quickly.

(f) Avogadro’s law:It states that under similar conditions of pressure and temperature, equal volume of all gases contain equal

number of molecules.

For m gram of gas, PV/T = nR = (m/M) R

Pressure of a gas (P):P = 1/3 (M/V) C2 = 1/3 (ρ) C2

• Root mean square (r.m.s) velocity of the gas:Root mean square velocity of a gas is the square root of the mean of the squares of

the velocities of individual molecules.

C= √[c12+ c22+ c32+…..+ cn2]/n = √3P/ ρ

• Pressure in terms of kinetic energy per unit volume:The pressure of a gas is equal to two-third of kinetic energy per unit

volume of the gas.

P= 2/3 E

• Kinetic interpretation of temperature:Root mean square velocity of the molecules of a gas is proportional to the square root of

its absolute temperature.

C= √3RT/M

At, T=0, C=0

Thus, absolute zero is the temperature at which all molecular motion ceases.

• Kinetic energy per mole of gas:

K.E. per gram mol of gas = ½ MC2 = 3/2 RT

• Kinetic energy per gram of gas:

½ C2 = 3/2 rt

Here, ½ C2 = kinetic energy per gram of the gas and r = gas constant for one gram of gas.

• Kinetic energy per molecule of the gas:

Kinetic energy per molecule = ½ mC2 = 3/2 kT

Here, k (Boltzmann constant) = R/N

Thus, K.E per molecule is independent of the mass of molecule. It only depends upon the absolute temperature of the gas.

(a) Most probable speed:It is the speed, possessed by the maximum number of molecules of a gas contained in an enclosure.

Vm= √[2kT/m]

(b) Average speed (Vav):Average speed of the molecules of a gas is the arithmetic mean so the speeds of all the molecules.

Vav= √[8kT/πm]

(c) Root mean square speed (Vrms):It is the square root of the mean of the squares of the individual speeds of the molecules of a gas.

Vrms = √[3kT/m]

Vrms >Vav >Vm

• Degree of Freedom (n):Degree of freedom, of a mechanical system, is defined as the number of possible independent ways, in

which the position and configuration of the system may change.

In general, if N is the number of particles, not connected to each other, the degrees of freedom n of such a system will be,

n = 3N

If K is the number of constraints (restrictions), degree of freedom n of the system will be,

n = 3N –K

• Degree of freedom of a gas molecule:

(a)Mono-atomic gas: Degree of freedom of monoatomic molecule, n = 3

(b)Di-atomic gas:

At very low temperature (0-250 K): Degree of freedom, n = 3

At medium temperature (250 K – 750 K): Degree of freedom, n = 5 (Translational = 3, Rotational = 2)

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At high temperature (Beyond 750 K): Degree of freedom, n = 6 (Translational = 3, Rotational = 2, Vibratory =1), For calculation

purposes, n = 7

• Law of equi-partition of energy: In any dynamical system, in thermal equilibrium, the total energy is divided equally among all

the degrees of freedom and energy per molecule per degree of freedom is ½ kT.

E = ½ kT

• Mean Energy:Kinetic Energy of one mole of gas is known as mean energy or internal energy of the gas and is denoted by U.

U = n/2 RT

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Practice Questions 1. Which of the following is a measure of hotness of a body?

(a) Temperature (b) Heat

(c) specific head (d) Latent heat

2. A glass of ice-cold water left on a table on a hot summer

day eventually warms up whereas a cup of hot tea on the

same table cools down because.

(a) its surrounding media are different

(b) the direction of heat flow depends on the

surrounding temperature with respect to the object

(c) the variation of the resistance of a wire with

temperature

(d) All of the above

3. The ice point and the steam point of water are two

convenient fixed points and are known as the

(a) cooling point and heating point, respectively

(b) heating point and cooling point, respectively

(c) freezing point and boiling point, respectively

(d) boiling point and freezing point, respectively.

4. At the freezing and boiling points.

(a) pure water freezes and boils under standard

pressure, respectively

(b) salty water freezes and boils under standard

pressure respectively

(c) Both (a) and (b)

(d) neither (a) nor (b)

5. A fully inflated balloon shrinks when it is put into cold

water, because.

(a) water causes lesser pressure from outside on the

balloon.

(b) water causes a pull on balloon which presses it

(c) air inside the balloon contracts due to cooling

(d) rubber of balloon expands on cooling and

compresses air inside.

6. When water boils or freezes, during these processes its

temperature

(a) increases

(b) decreases

(c) does not change

(d) sometimes increases & sometimes deceases

7. Steam burns are more serious as

(a) steam at 100°C carries same heat as that of water

100°C but pressure of steam is more.

(b) steam is more reactive.

(c) steam has less surface tension and so it burns surface

more rapidly

(d) steam at 100°C carries more heat than water at

100°C

8. A point at which vaporisation curve, fusion curve and

sublimation curve meet, is called.

(a) melting point (b) boiling point

(c) freezing point (d) triple point

9. Triple point of water is

(a) 273.16 K temperature and 1 atm pressure.

(b) 273.16 K temperature and 6.11×10-3 atm pressure.

(c) 4°C temperature and 76 cm of Hg pressure

(d) STP

10. Hot water or milk when left on a table begins to cool

gradually, because

(a) temperature of surroundings is higher

(b) everything cools down with time irrespective of the

temperature of the surroundings

(c) temperature of surroundings is lesser.

(d) None of the above

11. The rate of loss of heat depends on

(a) the sum of temperature of the body and its

surroundings

(b) the difference of the body and its surroundings

(c) the product of temperature of the body and its

surroundings

(d) the ratio of temperature of the body and its

surroundings.

12. On a hilly region, water boils at 95°C. The temperature

expressed in Fahrenheit is

(a) 100°F (b) 20.3°F

(c) 150°F (d) 203°F

13. When the pressure is held constant, the volume of a

quantity of the gas is related to the temperature as V/T =

constant. This is known as

(a) Boyle’s law

(b) Dalton partial pressure law

(c) Charles law

(d) Ideal gas equation

14. Measurements on real gases deviate from the values

predicted by the ideal gas law at

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(a) high temperature (b) low temperature

(c) room temperature (d) All of these

15. The absolute minimum temperature for an ideal gas,

therefore inferred by extrapolating the straight line to

the temperature axis, is called as

(a) Kelvin temperature

(b) Celsius temperature

(c) low temperature

(d) absolute zero

16. When temperature of water is raised from 0°C to 4°C, it

(a) expands

(b) contracts

(c) expands upto 2°C and then contracts upto 4°C

(d) contract upto 2°C and then expands upto 4°C

17. Which of the following graph shows the variation of

volume of water with increase in temperature?

18. Temperature of atmosphere is Kashmir falls below –

10°C in winter. Due to this water animal and plant life of

Dal-lake

(a) is destroyed in winters

(b) frozen is winter and regenerated in summers

(c) survives as only top layer of lake in frozen


19. When water changes to ice, the temperature of system

(water ⇌ ice)

(a) decreases

(b) increases

(c) remains same

(d) state change has no relation with temperature

20. When water changes to water vapour, then

(a) no temperature change takes place

(b) no heat flow occurs

(c) heat flows into the water from surrounding heat

source

(d) Both (a) and (c)

21. Time taken to heat water upto a temperature of 40°C

(from room temperature) is t1 and time taken to heat

mustard oil (of same mass and at room temperature)

upto a temperature of 40°C is t2, then (given mustard oil

has smaller heat capacity)

(a) t1 = t2

(b) t1> t2

(c) t2> t1

(d) t1 and t2 both are less than 10 min

22. Amount of heat required to warm an object depends on

(a) mass of object

(b) temperature change

(c) nature of substance

(d) All of these

23. A good coolant must have

(a) low specific heat (b) high specific heat

(c) low density (d) high density

24. A block of ice at 0°C is slowly heated and converted into

steam at 100°C. Which of these curves represents the

phenomenon qualitatively?

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25. At atmospheric pressure, water boils at 100°C. If

pressure is reduced, then

(a) it still boils at same temperature

(b) it now boils at a lower temperature

(c) it now boils at a higher temperature

(d) it does not boil at all

26. A liquid boils when its vapour pressure is equal to

(a) 6.0 cm of Hg column

(b) atmospheric pressure

(c) double of atmospheric pressure

(d) 1000 Pa or more

27. Cooking is difficult on hills because

(a) atmospheric pressure is higher

(b) atmospheric pressure is lower

(c) boiling point of water is reduced

(d) Both (b) and (c)

28. Change of state from solid to vapour state without

passing through the liquid state is called

(a) regelation (b) sublimation

(c) condensation (d) sedimentation

29. The latent heat of vaporization of a substance is always

(a) greater than its latent heat of fusion

(b) greater than its latent heat of sublimation

(c) equals to its latent heat of sublimation

(d) less than its latent heat of fusion

30. For the phase diagram of water given in figure, curves

OA, AB and AC are respectively?

(a) Sublimation curve, vaporization curve and fusion

curve

(b) Sublimation curve, fusion curve and vaporization

curve

(c) Fusion curve, vaporization curve and Sublimation

curve,

(d) Fusion curve, Sublimation curve and vaporization

curve

31. The amount of heat that a body can absorb by radiation.

(a) depends on colour and temperature both of body.

(b) depends on colour of body only

(c) depends on temperature of body only

(d) depend on density of body

32. The bottoms of utensils for cooking food are blackened

to

(a) absorb minimum heat from fire

(b) absorb minimum heat from fire

(c) emit radiation

(d) reflect heat to surroundings

33. A liquid in a beaker has temperature θ(t) at time t and θ0

is temperature of surroundings, then according to

Newton’s law of cooling, the correct graph between loge

= (θ – θ0) and t is

34. Specific heat capacity of a substance depends on

I. mass of substance. II. Nature of substance.

III. rise in temperature IV. Volume of substance.

(a)I and II (b) II and III

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(c) III and IV (d) I and IV

35. During vaporization,

I. the change of state from liquid to vapour state occurs.

II. the temperature remains constant.

III. both liquid and vapour states coexist in equilibrium.

IV. specific heat of substance increases.

Correct statements are

(a) I, II and IV (b) II, III and IV

(c) I, III and IV (d) I, II, III and IV

36. Which of the following statement(s) is/are correct?

I. Gases are poor thermal conductors.

II. Liquids have conductive intermediate between solids

and gases.

III. Heat conduction can take place from cold body to

hotter body.

(a) Only I (b) Only II

(c) Only III (d) Both I and II


I. Convection is a mode of heat transfer by actual motion

of matter.

II. Convection is possible only in gases.

III. Convection can be natural of forced.

(a) Only I (b) Both I and III

(c) Only II (d) All of these

38. The common example of forced convection system are

I. human blood circulatory system.

II. cooling system of an automobile engine.

III. human-liver system.

IV. water cycle.

(a) Only I (b) Both I and II

(c) I, II and IV (d) Both II and III


I. Thermos bottle consists of a double-walled glass vessel

with inner and outer walls coated with silver.

II. In flask, space between the walls is evacuated to

reduced conduction and convection losses.

III. Thermos bottle is useful for preventing hot contents

(like milk) from getting cold or to store cold content (like

ice).

(a) Only I (b) Only II

(c) Both I and II (d) All of these


I. Conduction of heat takes places in solids and liquids

like mercury and molten metals.

II. In radiation energy directly flows from heat source to

the given body at a speed of 3 × 108 ms-1.

III. Convection of heat takes place in liquids only.

(a) Only I (b) Both II and III

(c) Only III (d) Both I and II

41. Match Column I and Column II as per the anomalous

behavior of water and choose the correct options from

codes given.

Column I Column II

A. Density maximum 1. 4°C

B. Volume increases 2. 27°C to 10°C

C. Volume decreases 3. 4°C to 0°C

D. Density increases 4. 0°C to 4°C

A B C D A B C D

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(a) 1 3 2 4 (b) 1 2 3 4

(c) 1 4 3 2 (d) 1 4 2 3

42. If there is a rise in temperature θ, then time period of

pendulum

(a) increases (b) decreases

(c) no change (d) cannot be determined

43. A sphere, a cube and a thin circular plate, all of same

material and same mass are initially heated to same high

temperature.

(a) Plate will cool faster cube the slowest

(b) Sphere will cool fastest and cube the slowest

(c) Plate will cool fastest and sphere the slowest

(d) Cube will cool fastest and plate the slowest

44. Gulab jamuns (assumed to be spherical) are to be heated

in an oven. They are available in two size, one twice

bigger (in radius) than the other. Pizzas (assumed to be

discs) are also to be heated in oven. They are also in two

sizes, one twice bigger (in radius) than the other. All four

are put together to be heated to over temperature.

Choose the correct option from the following.

(a) Both size gulab jamuns will get heated in the same

time

(b) Smaller gulab jamuns are heated before bigger ones

(c) Smaller pizzas are heated before bigger ones

(d) Bigger pizzas are heated before smaller

45. Interatomic forces are

(a) attractive in long range

(b) repulsive in short range

(c) negligible in gases

(d) All a, b and c

46. According to atomic hypothesis

(a) atoms attract each other when they are little distance

apart

(b) atoms repel if they being squeezed into one another

(c) Both (a) and (b)

(d) Neither (a) nor (b)

47. Choose the correct option.

(a) Avogadro's law with Dalton theory could explain Gay

Lussac's law

(b) Dalton's atomic theory could also be termed as

molecular theory as well

(c) Initially Dalton's theory was not accepted by other

scientists


48. Which of the following option is correct about the flow of

a liquid?

(a) In liquids the atoms are not as rigidly fixed as in solid

(b) In liquids the atoms are more rigidly fixed as in gas

(c) In liquid the separation between atoms arespaced

about Å


49. A real gas behaves like an ideal gas if its

(a) pressure and temperature are both high

(b) pressure and temperature are both low.

(c) pressure is high and temperature is low

(d) pressure is low and temperature is high.

50. Kinetic theory of gases

(a) correctly explains specific heat capacities of many

gases

(b) relates properties of gases such as viscosity ,

conduction etc., with molecular parameters

(c) Both (a) and (b) are correct.

(d) None of these


(a) Maxwell and Boltzmann were among the scientists

who developed kinetic theory

(b) Kinetic theory gives molecular interpretation of

pressure and temperature of a gas

(c) Kinetic theory is consistent with gas laws and

Avogardro's hypothesis


52. The collisions of the molecules of an ideal gas are

(a) elastic (b) inelastic

(c) total KE and total momentum remains conserved

(d) Neither total KE nor total momentum is conserved.


(a) In derivation of pressure the shape of vessel doesn't

matter.

(b) Pressure of gas in equilibrium is same everywhere

(c) In derivation of pressure we neglect the collisions

between the molecules as it doesn't make much

difference


54. The internal energy of ideal gas is in form of

(a) kinetic energy of molecules

(b) potential energy of molecules.

(c) both kinetic and potential energy of molecules

(d) gravitational potential energy of molecules

19




55. According to the kinetic theory of gases, the temperature

of a gas is measure of average

(a) velocities of its molecules

(b) linear momenta of its molecules

(c) kinetic energies of its molecules

(d) angular momenta of its molecules

56. The internal energy of an ideal gas depends on

(a) pressure (b) volume

(c) mass (d) temperature

57. The mass of 22.4L of O2 at STP is

(a) 32 kg (b) 16 g (c) 32 g (d) 16 mg

58. Which one of the following graphs represents the

behavior of an ideal gas?

59. Match the following.

Column I Column II

A. pV = kBNT 1. Gay-Lussac’s law

B. p ∝ 1/V

T = constant

2. Boyle’s law

C. p ∝ T

V = constant

3. Ideal gas equation

D. V ∝ T

p = constant

4. Charles’ law

A B C D A B C D

(a) 3 2 1 4 (b) 3 3 1 4

(c) 3 2 4 1 (d) 3 2 1 4

60. Which of the following diagrams (figure) depicts ideals

gas behavior?

20




ANSWER KEY

1 A 2 B 3 C 4 A 5 C

6 C 7 D 8 D 9 B 10 C

11 B 12 D 13 C 14 B 15 D

16 B 17 B 18 C 19 C 20 D

21 B 22 D 23 B 24 D 25 B

26 B 27 D 28 B 29 A 30 B

31 A 32 B 33 A 34 B 35 D

36 D 37 B 38 B 39 D 40 D

41 A 42 A 43 C 44 BC 45 D

46 C 47 D 48 A 49 D 50 C

51 D 52 A 53 D 54 A 55 C

56 D 57 C 58 D 59 D 60 AC

SOLUTION

1. (a) Temperature is a measure of hotness of a body. A body at

a higher temperature when touched gives a feeling of

more hotness than that at a lower temperature. But,

temperature does not give the measure of content of

heat in a body.

2. (b) When the temperature of body, ice cold water or hot tea

in this case, and its surrounding medium are different,

then heat transfer take place between the system and the

surrounding medium, until the body and the

surrounding medium are at the same temperature

3. (c) The ice point and the steam point of water are two

convenient fixed points and known as the freezing and

boiling points. These two points are the temperature at

which pure water freezes and boils respectively under

standard pressure.

4. (a) On the freezing and boiling points, pure water freezes

and boils respectively under standard pressure.

5. (c) Air inside the balloon contracts and therefore balloon

walls shrink. A change in temperature of a body causes a

change in dimensions.

6. (c) When water boils or freezes, its temperature does not

change during these processes. Heat is absorbed or

librated as latent heat.

7. (d) For water, the latent heat of fusion and vaporization are

Lf = 3.33 × 105 J kg-1 and Lv = 22.6 × 105 J kg-1,

respectively. That is 3.33 × 105 J of heat is needed to melt

1 kg of ice at 0°C, and 22.6 × 105 J of heat is needed to

convert 1 kg of water to steam at 100°C. This is why

burns from steam are usually more serious than those

from boiling water.

8. (d) At triple point matter exists in all three states,

i.e., vapour state, solid state and liquid state.

9. (b) Triple point of water is 273.16 K temperature and 6.11 ×

10-3 atm pressur.

10. (c) Hot water or milk when left on a table begins to cool

gradually because it loses the heat to the surroundings.

11. (b) The rate of loss of heat depends on the difference in

temperature between the body and its surroundings.

12. (d) Given, C = 95°C, F = ?

Using relation 32

,180 100

F C we get

32 95

9 5

F

⇒F – 32 = 171⇒F = 171 + 32 = 203°F

13. (c)

14. (b) Measurements on real gases deviation from the values

predicted by the ideal gas law at low temperature. But,

the relationship is linear over a large temperature range,

and it looks as though the pressure might reach zero

with decreasing temperature, if the gas continued to be a

gas.

15. (d) The absolute minimum temperature for an ideal gas,

therefore, inferred by extrapolating the straight line to

the temperature axis, as in figure. This temperature is

found to be – 273.15°C and is designated as absolute

zero.

16. (b) Water contracts when it is heated from 0°C to 4°C, its

volume is least at 4°C.

17. (b) Water contracts when is heated from 0°C to 4°C.

Thus, its density increases. Density of water is maximum

at 4°C. when the water is further heated, it expands and

volume thus increases.

18. (c) Ice formed floats over surface, it exerts pressure over

water below causing lowering of freezing point and ice

layer on top also acts like an insulator. Bottom of lake

remains in liquid state due to above reason.

19. (c) During state change, the temperature of the system

remains same.

20. (d) When water boils or freezes, its temperature does not

change during these processes but heat transfer takes

place.

21. (b) Time taken to heat mustard oil is much less than that

required by the same amount of water for the same rise

in temperature.

22. (d) The quantity of heat required to warm a given substance

depends on its mass m, the change in temperature ΔT

and the nature of substance.

21




23. (b) Water has the highest specific heat capacity compared to

other substances. For this reason, water is used as a

coolant in automobile radiators as well as a heater is hot

water bags.

Owing to its high specific heat capacity, the water warms

up much slowly, than the other liquids.

24. (d) A plot of temperature versus time showing the changes

in the state of ice on heating (not to scale).

O → A : Solid + liquid

A → B : liquid

B → C : liquid + gas

C → D : gas

25. (b) When pressure is increased, boiling point is elevated. i.e.,

at higher pressure, water boils at temperature greater

than 100°C. similarly, at reduced pressure, water boils at

a lower temperature.

26. (b) When vapour pressure is equal to atmosphere pressure,

then boiling occurs.

27. (d) At high altitudes, atmospheric pressure is lower,

redacting the boiling point of water as compared to that

at sea level. When boiling point of water is reduced, it

has lesser heat at boiling, it transfers lesser heat to raw

food material, per unit time. So, it takes more time to

cook food.

On the other hand, boiling point is increased inside a

pressure cooker by increasing the pressure. Hence,

cooking is faster.

28. (b) Sublimation is conversion of a solid into vapour without

being liquid.

29. (a) As more energy is required for enormous expansion.

When a substance is changed from liquid to gaseous

state, latent heat of vaporization is always greater than

latent heat of fusion.

30. (b) The point on the sublimation curve OA represents states

in which the solid and vapour phases coexist. Points on

the fusion curve AB represent states in which solid and

liquid phase coexist.

31. (a) The thermal radiation that falls on a body partly

reflected and partly absorbed. The amount of heat that a

body can absorb, by radiation depends on the colour of

the body and temperature of body.

32. (b) Black bodies absorb and emit radiant energy better than

bodies of lighter colours. The bottoms of the utensils for

cooking food are blackened so that they absorb

maximum heat from the fire and give it to the vegetables

to be cooked.

33. (a) According to Newton’s law of cooling, rate of fall in

temperature is proportional to the difference in

temperature of the body with surroundings, i.e.

-d

dt

= h (θ – θ0)

⇒0

dk dt

⇒In (θ – θ0) = -kt + C

Which is a straight line with negative slope.

34. (b) If ΔQ stands for the amount of heat absorbed or rejected

by a substance of mass m when it undergoes a

temperature change ΔT, then the specific heat capacity of

that substance is given by

C =1 Q

m t

The specific heat capacity is the property of the

substance which determines the change in the

temperature of the substance (undergoing no phase

change) when a given quantity of heat is absorbed (or

rejected) by it. Also, specific heat of vapour state is more

than that of liquid state.

22




35. (d) The change of state from liquid to vapour (for gas) is

called vaporisatin. It is observed that when liquid is

heated, the temperature remains constant until the

entire amount of the liquid is converted into vaopur.

That is, both the liquid and vapour states of the

substance coexist in thermal equilibrium, during the

change of state from liquid to vapour. The temperature

at which the liquid and the vapour states of the

substance coexist is called its boiling point.

36. (d) Gases are poor thermal conductors while liquids have

conductivities intermediate between solids and gases.

Conduction takes place from hot to cold body.

37. (b) Convection is a mode of heat transfer by actual motion of

matter. It is possible only in fluids. Convection can be

natural or forced. In natural convection, gravity plays an

important part.

38. (b) The common examples of forced convection system are

forced-air heating system in home, the human

circulatory system and the cooling system of an

automobile engine.

In the human body, the heart acts as the pump that

circulates blood through different parts of the body,

transferring heat by forced convection and maintaining it

at a uniform temperature.

39. (d) In thermos bottle, radiation from the inner wall is

reflected back into the contents of the bottle. The outer

wall similarly reflects back any incoming radiation. The

space between the walls is evacuated to reduce

conduction and convection losses and the flask is

supported on an insulator like cork.

The device is, therefore useful for preventing hot

contents (like milk) from getting cold or alternatively to

store cold contents (like ice).

40. (d) Three modes of heat transmission are conduction,

convection and radiation.

S.

No.

Conduction Convection Radiation

1. There is no

bodily

motion of

medium

particles.

Medium

particles

vibrate to

and fro

about their

mean

positions

and pass on

Heat is

transferred

from one

part of

system to

another by

the actual

motion of

the

particles of

the system.

Medium has no

role as thermal

radiations are

transmitted

without any

material

medium.

thermal

energy to the

neighbouring

particles.

2. Conduction

of heat takes

place in

solids and

liquids like

mercury and

molten

metals.

Convection

of heat

takes place

in fluids,

i.e., liquids

as well as

gases.

Radiant energy

directly flows

from heat

source to the

given body at a

speed of 3 × 108

ms-1 as

electromagnetic

waves.

41. (a) Density of water is maximum at 4°C ⇒ A → 1.

∴ Voltage decreases when water is cooled from 27°C to

10°C. Also, if water is heated from 0°C to 4°C, its density

increases and volume decreases C → 4 and D → 4.

Volume increases when water is cooled down from 4°C

to 0°C ⇒ B → 3. Also, density decreases from 4°C to 0°C.

42. (a) Given, time period of a simple pendulum

T = 2πl

g i.e.,T ∝ l

since, when temperature is increased, length of the

pendulum increases and hence, the time period

increases.

43. (c) Consider the diagram where all the three objects are

heated to same temperature T. We know that density, =

mass

volume

volume will also be same.

As thickness of the plate is least hence, surface area of

the plate is maximum.

We know that according to Stefan’s law of heat loss H ∝

AT4

where, A is surface area for object and T is temperature.

Hence,Hsphere :Hcube : Hplate

= A sphere : A cube : A plate

As A plate is maximum.

Hence, the plate will cool fastest.

As, the sphere is having minimum surface area hence, the

sphere cools slowest.

44. (b, c) Smaller gulab jamuns are having least surface area

hence, they will be heated first.

As in case of smaller gulab jamun heat radiated will be

less.

23




Similarly, smaller pizzas are heated before bigger ones

because they are of small surface areas.

45. (d) Interatomic forces are attractive in long range and

repulsive in short range and negligible in gases.

46. (c) Atoms attract when they are little distance apart and

repel, if they being squeezed into one another.

47. (d) Avogadro’s law say Equal volumes of all gases at equal

temperature and pressure have the same number of

molecules. Avogadro’s law, when combined with

Dalton’s theory explains Gay Lussac’s law. Dalton’s

atomic theory can also be referred to as the molecular

theory of matter. The theory is now well accepted by

scientists. However even at the end of the nineteenth

century there were famous scientist who did not believe

in atomic theory.

48. (a) In liquids the atoms not as rigidly fixed as in solid, and

can move around. The enables a liquid to flow.

49. (d) A real gas behaves like an idea gas at low pressure and

high temperature.

50. (c) Kinetic theory of gases correctly explains specific heat

capacities of many gases and it relates properties of

gases viscosity, conduction etc., with molecular

parameter.

51. (d) The kinetic theory was developed in the nineteenth

century by Maxwell, Boltzmann and others. It has been

remarkably successful. It gives a molecular

interpretation of pressure and temperature of a gas is

consistent with gas laws and Avogadro’s hypothesis.

52. (a) According to kinetic theory of gases the collision among

molecules and the collision of molecules with the walls of

container are elastic.

53. (d) The collision of molecules will not make any difference in

the expression of pressure because

(i) the distribution of velocities will not change even

after collision as gas is in steady state.

(ii) we find 2

xv , so by taking average we reduce the

change of error.

54. (a) As in an ideal gas molecular interaction is negligible, the

concept of potential energy of molecular will not work

here. So, the internal energy will depend only on the

kinetic energy of the molecules.

55. (c) According to kinetic theory of gases the temperature of a

gas is a measure of the average kinetic energies of the

molecules of the gas.

56. (d) Internal energy of an ideal gas depends only on the

temperature of the gas.

57. (c) The mass of 22.4 L of any substance at STP is equal to its

molecular weight in grams.

So, M (O2) = 32 g

58. (d) For an ideal gas keeping the temperature same

throughout,

pV = constant

hence, for a given mass, the graph between pV and V will

be a straight line parallel to V-axis whatever may be the

volume.

59. (d) According to Boyle’s law p1V1 = p2V2 = constant.

According to Charles’ law 1 2

1 2

V V

T T = constant. Also,

according to ideal gas equation p1V1 = kNT.

60. (a, c) We know that ideal gas equation is

pV = nRT … (i)

(a) When pressure, p = constant

From Eq. (i) volume V ∝ Temperature T

(b) When T = constant

From Eq. (i) pV = constant

(c) When V = constant.

From Eq. (u) p ∝ T

So, the graph is straight line passes through the origin.

(d) From Eq. (i) pV ∝ T

⇒ pV

T= constant ⇒ So, the graph hence, through origin.

SSC CDS

BANKrAILWAY



Physics



1999 to till date

C L A S S E S

Chapter - 18

(Hydrostatics & Hydrodynamics)

1




HYDROSTATICS AND HYDRODYNAMICS Pressure

The force acting per unit area on a surface is known as

pressure.

Pressure (p) = Force (F)

Area (A)

It is a scalar quantity having SI unit Nm–2 or Pascal

(Pa).

Fluid is the name given to a substance which begins to flow when external force is applied on it.

Pressure in Liquid

The pressure at any point inside the liquid acts in all directions. Pressure at a depth h in a liquid of density p is given by

P = pgh + P0

where, g = acceleration due to gravity

p = density of liquid

h= height of liquid column

and P0 = atmospheric pressure.

Floatation and swimming in sea water is easier due to its high density than fresh water.

At higher altitudes, atmospheric pressure is lower than that at sea level.

Archimedes' Principle

It states that when a body is immersed wholly or partly in a liquid at rest, it loses some of its weight. The loss in weight of the body

in the liquid is equal to the weight of the liquid displaced by the immersed part of the body.

Note: The upward force exerted by a fluid on the immersed body is called buoyant force or buoyancy or upthrust.

Density

The ratio of mass m to the volume V of a body is called its density (i.e. mass present in its unit volume). It is a scalar quantity having

SI unit - kg/m3.

The density of water is 1000 kg/m3 (at 40C).

Density (p) = Mass (m)

Volume (V)

Law of Floatation

When a body of density , volume V is immersed completely in a liquid of density , two

forces are acting on it.

1. True weight W (= V g) of the body acting vertically downwards through the centre of

gravity.

2. Buoyant force or upward thrust w (= V g), equal to the weight of the liquid displaced,

acting vertically upward through the centre of Buoyancy.

The observed weight of the body immersed into the liquid = W – w = V g – V g.

If W > w, then W – w is positive. In this case, the body will sink to the bottom of the liquid.

If the body is not hollow from inside, then the density of solid body is greater than the

density of liquid (i.e., >).

2




If W < w, then W – w is negative. In this case, the body will rise above the surface of liquid to such an extent that the weight of the

liquid displaced by the immersed part of the body (i.e., upward thrust) becomes equal to the weight of the body. The body then will

float. In this case the density of solid body is less than the density of liquid (i.e., <).

If W = w, then W – w = 0. It means the resultant force acting on the body fully immersed in the liquid in zero. In this case, the body

is at rest anywhere within the liquid. The apparent weight of the body is zero at all positions inside the liquid. In this situation, the

body will float if its whole volume is just immersed in the liquid. If the body is solid then the density of body is equal to the density

of liquid (i.e., = ).

Thus the law of floatation states that a body will float in a liquid, if weight of the liquid displaced by the immersed part of the body

is atleast equal to or greater than the weight of the body.

There will be equilibrium of floating bodies if the following conditions are fulfilled.

(i) A body can float if the weight of the liquid displaced by the immersed part of body must be equal to the weight of the body.

(ii) A body can be in equilibrium if the centre of gravity of the body and centre of buoyancy must be along the same vertical line.

(iii) The body will be in stable equilibrium if centre of gravity of body lies vertically below the centre of buoyancy and in the

unstable equilibrium if centre of gravity lies vertically above the centre of buoyancy.

1. When an ice block is floating in water in a vessel, then the level of water in the vessel will not change when the whole ice melts into

water.

2. When an ice block is floating in a liquid in a vessel and ice completely melts, then the following cases may arise for the level of

liquid in the vessel.

(i) If density of liquid is greater than that of water, i.e., l>w, the level of liquid plus water will rise.

(ii) If density of liquid is less than the density of water, i.e., l<w, the level of liquid plus water will decrease.

(iii) If density of liquid is equal to the density of water, i.e., l = w, the level liquid plus water will remain unchanged.

Atmospheric Pressure

The air that envelopes the earth is called atmosphere and the pressure exerted by it on a body on the earth is called atmospheric

pressure.

3




The atmospheric pressure is maximum at the surface of the earth and goes on decreasing as we move up into the earth's

atmosphere. The measurement of atmospheric pressure is carried out by barometer.

Barometers are also used for weather forecasting. If the barometric height falls suddenly, it indicates the coming of a storm. A

gradual fall and rise in barometric height indicate the possibility of rain and fair weather respectively.

1 atmospheric pressure = 1.01 bar = 1.01 × 105 N/m2

A barometer is a device for measuring atmospheric pressure.

Pascal's Law

It states that if gravity of effect is neglected, the pressure at every point of

liquid in equilibrium of rest is same.

This law also accounts for the principle of transmission of pressure in

liquids or gases. In this form,

Pascal's law states that the increase in pressure at one point of the

enclosed liquid in equilibrium of rest is transmitted equally to all other

points of the liquid and also to the walls of the container, provided the

effect of gravity is neglected.

i.e P1 = P2

This applies to fluid at rest

Surface Tension

Thus, surface tension is the property of the liquid by virtue of which the free surface of liquid at rest

tends to have minimum surface area and as such it behaves as if covered with a stretched membrane.

Measurement of Surface Tension

Surface tension of a liquid is measured as the force acting on unit length of a line imagined to be drawn

tangentially anywhere on the free surface of the liquid at rest. It acts at right angles to this line on both

the sides and along tangent to the liquid surface.

S = F/l

Units of surface tension are dyne/cm in cgs system and Nm–1 in SI.

The dimensional formula of surface tension is [ML°T–2]. Surface tension is a scalar quantity because it has no specific direction for

a given liquid.

Illustrations of Surface Tension

1. Rain drops are spherical in shape because each drop tends to acquire minimum surface area due to surface tension, and for a given

volume, the surface area of sphere is minimum.

2. When mercury is split on a clean glass plate, it forms globules. Tiny globules are spherical on account of surface tension because

force of gravity is negligible.

3. When a greased iron needle is placed gently on the surface of water at rest, so that it does not prick the water surface ,the needle

floats on the surface of water despite its being heavier.

The weight of the needle is balanced by the vertical components of the forces of surface tension. If the water surface is pricked by

one end of the needle, the needle sinks down.

Surface tension of a liquid decreases with an increase in temperature.

Surface Energy

4




The potential energy of the molecules in the surface of liquid is called the surface energy.

Surface energy = T × ΔA

where, T = surface tension of liquid

ΔA = increase in surface area

Surface Film

It is the top most layer of liquid at rest with thickness equal to the molecular range.

Inter-Molecular Forces

The forces between the molecules of the substances are called intermolecular forces.

Types of Intermolecular Forces

There are two types of intermolecular forces.

(i) Force of Adhesion or Adhesive Force

It is the fore of attraction acting between the molecules of different substances.

Water wets the surface of a glass container. While writing, graphite from lead pencil sticks to

the paper on account of adhesive forces. Fevicol, cement etc are useful in glueing two surface.

(ii) Force of Cohesion or Cohesive Force

It is the force of attraction amongst the molecules of the same substance.

The solids have definite shape and size. It is due to strong forces of cohesion amongst their

molecules. Liquids have definite volume, but no definite shape. Therefore, cohesive forces in

case of liquids are lesser. Hence, cohesive forces amongst the molecule of a gas are minimum.

Mercury does not wet the surface of a glass container because the force of cohesion amongst

molecules of mercury is stronger than the force of adhesion between molecules of mercury and

glass.

The cohesive and adhesive forces are Vander Waal forces. These forces are different from

ordinary gravitational forces and do not obey inverse square law. The cohesive or adhesive

force varies inversely as the seventh power of distance between the molecules, i.e., the cohesive or adhesive force increases rapidly

with decrease in distance between the molecules.

Detergent and Surface Tension

The dirty greasy stains on the clothes cannot be cleared by simply washing the clothes in water. This is so because water does not

find its contact with greasy dirt and hence cannot wet such surfaces. By adding detergent or soap to water, the greasy dirt from

cloth can be easily cleaned.

(i) The molecules of the soap or detergent are hair pins shaped.

5




(ii) When soap or detergent is dissolved in water, then heads of the hair pins shaped molecules get attracted to water surface.

(iii) When clothes with greasy stains are dipped in detergent or soap mixed water, then the pointed ends of the hair pins shaped

molecules get attached to the molecules of the greasy stain. As a result of it, the water comes into contact with greasy stain and thus

a water greasy dirt interface is formed. Due to it, the greasy dirt is held suspended. It happens so because detergent molecules

reduce the surface tension between water and greasy stain.

(iv) When clothes are rinsed in water, then the greasy dirt is washed away by the running water.

Applications of Surface Tension

1. Since surface tension of soap solution is low, it can spread over large area. Hence it can wash clothes more effectively. Hot soap

solution proves still better as surface tension decreases further on heating.

2. For the same reason, surface tension of all lubricating oils and paints is kept low.

3. Stormy waves at sea are calmed by pouring oil on sea water.

4. In soldering, addition of 'flux' reduces the surface tension of molten tin, hence, it spreads.

5. Anticeptics like dettol have low surface tension, so they spread faster.

Capillarity

A tube with a fine and uniform bore throughout its length is called a capillary tube.

The phenomenon of rise or fall of liquid in a capillary tube is called capillarity.

Rise or fall of a liquid in a capillary tube is caused by surface tension and depends on the

relative magnitude of cohesion of the liquid and the adhesion of the liquid to the walls of the

containing vessel.

Liquids rise in tubes if they wet (adhesion > cohesion)

6




Liquids fall in tubes that do not wet (cohesion > adhesion).

Applications of capillary action

(i) The fine pores of a blotting paper act like capillary tubes. Ink rise in them leaving the paper dry.

(ii) A towel soaks water on account of capillarity action.

(iii) Oil rises in the long narrow spaces between the threads of a wick, because they act as fine capillaries.

(iv) Swelling of wood in rainy season, is due to rise of moisture from air, in the pores of wood.

(v) Ploughing of field is essential for preserving moisture in the soil. By ploughing, the fine capillaries in the soil are broken. Water

from within the soil shall not rise and evaporate off.

(vi) Sand is drier soil than clay. This is because holes between the sand particles are not so fine as compared to that of clay, as to

draw up water by capillarity action.

Piezometer: For measuring pressure inside a vessel or pipe in which liquid is there, a tube may be attached to the walls of

the container (or pipe) in which the liquid resides so liquid can rise in the tube. By determining the height to which liquid rises and

using the relation P = ρgh, gauge pressure of the liquid can be determined. Such a device is known as piezometer. To avoid capillary

effects, a piezometer's tube should be about 1/2 inch or greater.

Fluid

A fluid is a substance which deforms continuously under the action of shearing forces, however small they may be. Conversely, it

follows that:

If a fluid is at rest, there can be no shearing forces acting and, therefore, all forces in the fluid must be perpendicular to the planes

upon which they act.

Shear stress in a moving fluid

Although there can be no shear stress in a fluid at rest. Shear stresses are developed when the fluid is in motion. If the particles of

the fluid move relative to each other so that they have different velocities, causing the original shape of the fluid to become

distorted. If, on the other hand, the velocity of the fluid is same at every point, no shear stresses will be produced, since the fluid

particles are at rest relative to each other.

The differences between the behaviors of solids and fluids under an applied force are as follows:

(i) For a solid, the strain is a function of the applied stress, providing that the elastic limit is not exceeded. For a fluid, the rate of strain

is proportional to the applied stress.

7




(ii) The strain in a solid is independent of the time over which the force is applied and, if the elastic limit is not exceeded, the

deformation disappears when the force is removed. A fluid continues to flow as long as the force is applied and will not recover its

original form when the force is removed.

Fluid vs gas

Although liquids and gases both share the common characteristics of fluids, they have many distinctive characteristics of their own.

A liquid is difficult to compress and, for many purposes, may be regarded as incompressible. A given mass of liquid occupies a fixed

volume, irrespective of the size or shape of its container, and a free surface is formed if the volume of the container is greater than

that of the liquid.

A gas is comparatively easy to compress. Changes of volume with pressure are large, cannot normally be neglected and are related

to changes of temperature. A given mass of gas has no fixed volume and will expand continuously unless restrained by a containing

vessel. It will completely fill any vessel in which it is placed and, therefore, does not form a free surface.

Types of Fluids

1. Newtonian fluids:

Fluids which obey the Newton's law of viscosity are called as Newtonian fluids. Newton's law of viscosity is given by

τ = μ dv/dy

where τ = shear stress

μ = viscosity of fluid

dv/dy = shear rate, rate of strain or velocity gradient

All gases and most liquids which have simpler molecular formula and low molecular weight such as water, benzene, ethyl alcohol,

CCl4, hexane and most solutions of simple molecules are Newtonian fluids.

2. Non-Newtonian fluids:

Fluids which do not obey the Newton's law of viscosity are called as non-Newtonian fluids.

Generally non-Newtonian fluids are complex mixtures: slurries, pastes, gels, polymer solutions etc.,

8




Various non-Newtonian Behaviors:

Time-Independent behaviors:

Properties are independent of time under shear.

Bingham-plastic: Resist a small shear stress but flow easily under larger shear stresses. e.g. tooth-paste, jellies, and some slurries.

Pseudo-plastic: Most non-Newtonian fluids fall into this group. Viscosity decreases with increasing velocity gradient. e.g. polymer

solutions, blood. Pseudoplastic fluids are also called as Shear thinning fluids. At low shear rates(du/dy) the shear thinning fluid is

more viscous than the Newtonian fluid, and at high shear rates it is less viscous.

Dilatant fluids: Viscosity increases with increasing velocity gradient. They are uncommon, but suspensions of starch and sand

behave in this way. Dilatant fluids are also called as shear thickening fluids.

Physical properties of fluid

1. Viscosity:

The viscosity (μ) of a fluid measures its resistance to flow under an applied shear stress. Representative units for viscosity are

kg/(m.sec), g/(cm.se (c) (also known as poise designated by P). The centipoise (cP), one hundredth of a poise, is also a

convenient unit, since the viscosity of water at room temperature is approximately 1 centipoise.

The kinematic viscosity (v) is the ratio of the viscosity to the density:

Viscosity of liquids:

Viscosity of liquids in general, decreases with increasing temperature.

The viscosities (μ) of liquids generally vary approximately with absolute temperature T according to:

ln = a - b ln T

Viscosity of gases:

Viscosity of gases increases with increase in temperature.

The viscosity () of many gases is approximated by the formula:

= o(T/To)n

in which T is the absolute temperature, o is the viscosity at an absolute reference temperature To, and n is an empirical exponent

that best fits the experimental data.

The viscosity of an ideal gas is independent of pressure, but the viscosities of real gases and liquids usually increase with pressure.

Viscosity of liquids are generally two orders of magnitude greater than gases at atmospheric pressure. Fow example, at 25oC,

water = 1 centipoise and air = 1 x 10-2centipoise.

2. Vapor pressure:

9




The pressure at which a liquid will boil is called its vapor pressure. This pressure is a function of temperature (vapor pressure

increases with temperature). In this context we usually think about the temperature at which boiling occurs. For example, water

boils at 100oC at sea-level atmospheric pressure (1 atm abs). However, in terms of vapor pressure, we can say that by increasing

the temperature of water at sea level to 100oC, we increase the vapor pressure to the point at which it is equal to the atmospheric

pressure (1 atm abs), so that boiling occurs. It is easy to visualize that boiling can also occur in water at temperatures much below

100oC if the pressure in the water is reduced to its vapor pressure. For example, the vapor pressure of water at 10oC is 0.01 atm.

Therefore, if the pressure within water at that temperature is reduced to that value, the water boils. Such boiling often occurs in

flowing liquids, such as on the suction side of a pump. When such boiling does occur in the flowing liquids, vapor bubbles start

growing in local regions of very low pressure and then collapse in regions of high downstream pressure. This phenomenon is called

as cavitation

3. Compressibility and the Bulk modulus

All materials, whether solids, liquids or gases, are compressible, i.e. the volume V of a given mass will be reduced to V - V when a

force is exerted uniformly all over its surface. If the force per unit area of surface increases from p to p + p, the relationship

between change of pressure and change of volume depends on the bulk modulus of the material.

Bulk modulus (K) = (change in pressure) / (volumetric strain)

Volumetric strain is the change in volume divided by the original volume. Therefore,

(change in volume) / (original volume) = (change in pressure) / (bulk modulus)

i.e., -V/V = p/K

Negative sign for V indicates the volume decreases as pressure increases.

the concept of the bulk modulus is mainly applied to liquids, since for gases the compressibility is so great that the value of K is not

a constant.

Equation of continuity

A

b

a2, v2

a1, v1 Cross-sectional view of a pipe through which incompressible liquid is passing,

then Equation of continuity states that

volume of liquid entering = volume of liquid leaving

a1v1 = a2v2

a1 area of tube at point A

v1velocity of liquid at point A

a2area of tube at point B.

v2velocity of liquid at point B.

10




Practice Questions 1. The key property of fluids is that

(a) they offer very little resistance to shear stress

(b) their shape changes.

(c) they offer very large resistance to shear stress

(d) Both (a) and (b)

2. Average pressure pav is defined as

(a) av

Fp

A (b) av

Vp

F

(c) av

Ap

F (d)

av

Fp

V

3. Pressure is a ……. quantity.

(a) scalar (b) vector

(c) tensor (d) Either (a) or (c)

4. Dimensions of pressure are

(a) [ML –1T-2] (b) [ML2 T2]

(c) [ML 3T-1] (d) [M2L-1T-2]

5. If two liquids of same masses but densities 1 and

2

respectively are mixed, then density of mixture is given

by

(a) 1 2

2

(b) 1 2

1 22

(c) 1 2

1 2

2

(d) 1 2

1 2

6. If two liquids of same volume but different densities 1

and 2 are mixed, then density of mixture is given by

(a) 1 2

2

(b) 1 2

1 22

(c) 1 2

1 2

2

(d) 1 2

1 2

7. Pascal's law states that pressure in a fluid at rest is the

same at all points, if

(a) They are at the same height

(b) They are along same plane

(c) They are along same line

(d) Both (a) and (b)

8. Pressure is applied to an enclosed fluid. It is

(a) Increased and applied to very part of the fluid

(b) Diminished and transmitted to the walls of the

container

(c) Increased in proportion to the mass of the fluid and

then transmitted

(d) transmitted unchanged to every portion of the fluid

and the walls of container.

9. Pressure is applied to an enclosed fluid. It is

(a) Increased and applied to every part of the fluid

(b) diminished and transmitted to the walls of the

container

(c) increased in proportion to the mass of the fluid and

then transmitted

(d) transmitted unchanged to every portion of the fluid

and the walls of container

10. In a streamline flow,

(a) the speed of a particle always remains same.

(b) the velocity of a particle always remains same

(c) the kinetic energies of all the particles arriving at a

given point are the same.

(d) the potential energies of all the particles arriving at a

given point are the same

11. In a laminar flow, the velocity of the liquid in contact

with the walls of the tube is

(a) zero (b)maximum

(c) in between zero and maximum

(d) equal to critical velocity

12. We have three beakers A, B and C containing three

different liquids. They are stirred vigorously and placed

on a table. Then, liquid which is

(a) most viscous comes to rest at the earliest.

(b) most viscous comes to rest at the last.

(c) most viscous slows down earliest but comes to rest at

the last.

(d) All of them come to rest at the same time.

13. For a surface molecule,

(a) the net force on it is zero

(b) there is a net downward force

(c) the potential energy is less than that of a molecule

inside

(d) the potential energy is more than that of a molecule

inside.

14. Pressure is a scalar quantity, because

11




(a) it is the ratio of force to area and both force and area

are vectors.

(b) It is the ratio of the magnitude of the force to area

(c) It is the ratio of the component of the force normal to

the area.

(d) It does not depend on the size of the area chosen.

15. With increase in temperature, the viscosity of

(a) gases decreases (b) liquids increases

(c) gases increases (d) liquids decreases

16. Streamline flow is more likely for liquids with

(a) high density (b) high viscosity

(c) low density (d) low viscosity

17. The density of water at 40C is

(a) 1.0 × 103 kgm-3 (b) 4 × 102 kgm-3

(c) 6 × 103 kgm-3 (d) 3.2 × 103 kgm-3

18. As the temperature of water increases, its viscosity

(a) remains unchanged

(b) decreases

(c) increases

(d) increases or decreases depending on the external

pressure

19. Surface tension is due to

(a) frictional forces between molecules

(b) cohesive forces between molecules

(c) adhesive forces between molecules

(d) Both (b) and (c)

20. The value of surface tension of water is minimum at

(a) 4°C (b) 25°C

(c) 50°C (d) 75°C

21. The surface tension of a liquid at its boiling point

(a) because zero

(b) becomes infinity

(c) is equal to the value at room temperature

(d) is half to the value at the room temperature

22. Why are drops and bubbles spherical?

(a) Surface with minimum energy

(b) Surface with maximum energy

(c) High pressure

(d) Low pressure

23. Match physical quantities in Column I with their

dimensions given in Column II

Column I Column II

A. Coefficient of

viscosity

1. [ML0T-2]

B. Density 2. [M0L0T0]

C. Surface tension 3. [ML-1T-1]

D. Reynold’s number [ML-3T0]

A B C D A B C D

(a) 2 3 4 1 (b) 1 3 4 3

(c) 3 4 1 2 (d) 1 2 3 4

24. Match the following Column I and Column II.

Column I Column II

A. Hydraulic lift 1. Archimedes’

principle

B. A razor blade can be

made to float on water

surface in a tray.

2. Pascal’s law

C. The dam of water

reservoir is made thick

at the bottom level.

3. Surface tension

D. Ship is floating on

ocean water.

4. Pressure

A B C D A B C D

(a) 2 3 4 1 (b) 2, 4 3 4 1

(c) 4 1 3 4 (d) 4,1 2 3 4

25. Which of the following diagrams does not represent a

streamline flow?

12




ANSWER KEY

1 D 2 A 3 A 4 A 5 C

6 A 7 A 8 D 9 D 10 B

11 A 12 A 13 BD 14 BC 15 CD

16 BC 17 A 18 B 19 D 20 A

21 A 22 A 23 C 24 A 25 D

SOLUTION 1. (d) The key property of fluids is that they offer very little

resistance to shear stress. So, their shape changes by

application of very small shear stress.

2. (a) If F is the magnitude of the normal force acting over an

area A, then the average pressure p is defined as the

normal force acting per unit area.

Pav =F

A

3. (a) Pressure is a scalar quantity. It is the component of the

force normal to the area under consideration and not the

(vector) force that appear in the numerator.

4. (a) Dimensions of pressure are [ML-1T-2]. The SI unit of

pressure is Nm-2.

5. (c) =1 2

1 2

2 2

1 1

Total mass m m

Total volume V V

∴ = 1 2

1 2

2

6. (a) = 1 21 2 1 2mass

2 2 2

Vm mTotal

Total volume V V

7. (a) Pascal’s law states that pressure in a fluid at rest is the

same at all points if they are at the same height.

8. (d) Pascals’ law

p =F

A= gh

∴ It does not depend on the weight of fluid.

9. (d) Pascals’ law

p =F

A= gh

∴ It does not depend on the weight of fluid.

10. (b) Both speed and direction of flow remain same.

11. (a) Most viscous fluid comes to rest quickly due to

dissipation of energy at a larger rate.

12. (a) Most viscous fluid comes to rest quickly due to

dissipation of energy at a larger rate.

13. (b, d)

Consider the diagram where two molecules of a liquid

are shown. One is well inside the liquid and other is on

the surface. The molecule (A) which is well inside

experiences equal forces from all directions, hence net

force on it will be zero.

And molecules on the liquid’s surface have some extra

energy as it surrounded sustained by only lower half side

of liquid molecules.

14. (b, c)

Pressure is defined as the ratio of magnitude of

component of the force normal to the area and the area

under consideration. As magnitude of component is

considered, hence it will not have any direction. So,

pressure is a scalar quantity.

15. (c, d) For liquids’ coefficient of viscosity, ∝1

T

i.e., with increase in temperature decreases.

For gases coefficient of viscosity, ∝ T

i.e., with increase in temperature increases.

16. (b, c) Streamline flow is more likely for liquids having low

density. We know that greater the coefficient of viscosity

of a liquid more will be velocity gradient hence each line

of flow can be easily differentiated. Also higher the

coefficient of viscosity lower will be Reynold’s number,

hence flow will be more likely to be streamline.

17. (a) The density of water at 40C (277 K) is 1.0 × 103 kgm3.

18. (b) For liquids, viscosity decreases with temperature.

19. (d) Both cohesive and adhesive forces result in surface

tension.

20. (a) Value of surface tension decreases with increase in

temperature.

13




21. (a) Surface tension is zero at boiling point.

22. (a) A liquid air interface has energy, so for a given volume

the surface with minimum energy is the one with the

least area.

23. (c) Density is mass per unit volume. Its dimension are [ML-

3T0].

The coefficient of viscosity has dimensions [ML-1T-1].

Reynold’s number is a dimensions number.

Surface tension is force per unit length. Hence, its

dimensions are [M L0T-2] Hence,

A → 3, B → 4, C → 1, D → 2

24. (a) A → 2, B → 3; C → 4; D → 1

Column I Column II

A. Hydraulic lift 2. Pascal’s law

B. A razor blade can be

made to float on water

surface in a tray

3. Surface tension

C. The dam of water

reservoir is made thick

at the bottom level

4. Pressure

D. Ship is floating on

ocean water

1. Archimedes’

principle

25. (d) In a streamline flow at any given point, the velocity of

each passing fluid particles remains constant. If we

consider a cross-sectional area, then a point on the area

cannot have different velocities at the same time, hence

two streamlines of flow cannot cross each other.

SSC CDS

BANKrAILWAY



Physics



1999 to till date

C L A S S E S

Chapter - 19

(Mechanical Properties of Solid)

1




MECHANICAL PROPERTIES OF SOLIDS Matter is anything that has mass and occupy space. It includes all the physical 'material' around us. Different matter have dissimilar

properties such as elasticity, density, viscosity, etc., to distinguish them from each other.

Stress

The restoring force per unit area is called stress. Its units is N/m2 or Pascal.

Stress = Restoring force (F)

Area (A)

There are different types of stress given as below

Normal Stress/Longitudinal Stress

Stress produced normal to the axis of the body is called normal stress. It consists of two types.

1. Compressive Stress: Stress produced in the body, which is responsible for the compression in the body is called compressive

stress.

2. Tensile Stress: Stress produced in the body, which is responsible for the elongation in the body is called tensile stress.

Shearing Stress and Volumetric Stress

Stress produced along the axis of the body under the action of a force parallel to its axis, i.e. tangential force is called shearing

stress. It is also called tangential stress.

Stress produced in the body under the action of the force, which is perpendicular to the surface and proportional to the area in case

the body is immersed in fluid, is called volumetric stress.

Strain

When a system of forces acts on a body, it undergoes some deformation. This deformation per unit length is known as unit strain or

simply a strain.

Strain is a ratio of change in dimension to the original dimension, it has no units or dimensional formula.

Strain = Changeinlength( l)

Original length (l)

There are three types of strain given as below

1. Longitudinal Strain:It is the ratio of change in length to that of initial length of the body (i.e. ΔL/L).

Force perpendicular to Area A must be considered when equal & opposite

force is applied on both ends. Then length increases.

Longitudinal Stress Pressure units

= = arF

Area

= Force perpendicular to Area

2




Longitudinal strain = l change in length

l Original length

3




2. Shear Strain

The angle between the displaced state and initial state of the body is called shearing strain. x

i.e.l

Force is applied parallel to surface

Shear stress = Force actingparallel to area F

Area A

E, Shear strain () = x

tanl

G, shear modules = Stress F l F

strain A x A

tan

3. Volumetric strain: It is the ratio of change in volume of the body to its initial volume (i.e. ΔV/V).

Volume Stress, P (Extra Pressure) = F

Area

Volume Strain, E = V

V

Bulk Modulus, B =Normal stress

volumetric strain=

F / a

V / V

Negative Sign is used because volume decreases once volumetric stress is applied.

Poisson's Ratio

When an object is streched, volume remains same so length but area (diameter )

Longitudinal strain =l Change in length

l Original length

Lateral strain =d Change in diameter

d Original diameter

It is the ratio of lateral strain to the longitudinal strain in a streched wire.

Poisson's ration (μ) = Lateral strain

Longitudinal strain=

d / d

l / l

Length , diameter

It is a dimensionless quantity.

Poisson's ratio for steel is 0.30.

Elasticity

The property of matter by virtue of which a body tends to regain its original shape and size after the removal of deforming force is

called elasticity.

If the body completely regains its original shape after removal of deforming force, the body is called perfectly elastic body.

Plasticity

The property of matter by virtue of which it does not regain its original shape and size after removal of deforming force is called

plasticity. If the body remains in deformed shape even after removal of the deforming force, it is called perfectly inelastic or

plastic body.

4




5




Note: Steel is more elastic than rubber because the magnitude of stress for a given strain is much large in steel than rubber.

Perfectly Plastic: Putty, mud, Paraffin Wax

Perfectly Elastic: Quartz,Phospher Bronze

Elastomer These are the materials which possess the qualities such as

• Stress vs Strain is not a straight line.

• Elastic Region is large.

• Ex. Rubber

Hooke's Law

According to this law,

within the elastic limits, the stress is directly proportional to the strain produced in a body.

i.e. Stress ∝ Strain or Stress = E × Strain

Stress

Strain= E

where, E is a constant called as Modulus of Elasticity (Proportionality constant)

It states that the extension produced in the wire is directly proportional to the load

applied, within elastic limit.

i.e., within elastic limit, extension load applied.

There are three Modulus of elasticity given as below

Young's Modulus of Elasticity (Y)

It is defined as the ratio of longitudinal stress to the longitudinal strain within the elastic limit. Thus,

Y = Longitudinal stress

Longitudinal strain

The SI unit of Young's modulus of elasticity is Nm-2 or Pascal (denoted by P a and in CGS system is dyne/cm2.

Bulk Modulus of Elasticity (B)

It is defined as the ratio of normal stress to the volumetric strain within the elastic limit. Thus,

6




7




B = Normal stress

Volumetric strain

The SI unit of bulk modulus of elasticity is Nm-2 or pascal (denoted by Pa and in CGS system is dyne/cm2.

Modulus of Rigidity (ɳ)

It is defined as the ratio of shearing stress to the shearing strain within the elastic limit. It is also called shear modulus of rigidity.

Thus, ɳ = Shearing stress

Shearing Strain

The SI unit of ɳ is Nm-2 or Pascal (denoted by P and in CGS system is dyne/cm2.

Note: Elastic hysteresis has an important application in shock absorbers.

Elastic Hysteresis. When a deforming force is applied on a body, then the strain does not change

simultaneously with stress, rather it lags behind the stress. The lagging of strain behind the stress is

defined as elastic hysteresis.

Stress-Strain Graph

• Upto Point A Proportional limit

Slope of this graph gives us Modulus of Elasticity , Hooke's Law is obeyed in this

region.

• A to B Elastic property of material is retained i.e. if you will remove stress,

material will regain its shape.

• B Elastic limit or yield limit

y Yield Stress: The value of stress on whose application we get yield point.

• After B If you stress, there is a much increase in strain & stress, if will

remove stress, material will not gain its original position.

• So, At C Object is permanently reformed at strain Permanent Set.

• After CSmall increase in stress gives larger value of strain.

• Dultimate Tensile strength

After this if we stress, strain .

• a point after D,At E fracture point object break.

If there is very small gap or No gap between D & E Object is brittle

If there is large gap between D & E Object is Malleable (sheets) and Ductile (wires)

Strain Energy = F e

2 ;

F maximum force acting on object

e elongation of object due to force

Strain energy volume = Stress Strain

2

E

8




Practice Questions 1. The property of a body by virtue of which it tends to

regain its original size and shape of a body when applied

force is removed, is known as

(a) fluidity (b) elasticity

(c) plasticity (d) rigidity

2. In solids, inter-atomic forces are

(a) totally repulsive

(b) totally attractive

(c) combination of (a) and (b)

(d) None of these

3. Elasticity is shown by materials because inter-atomic or

inter –molecular forces

(a) increases when a body is deformed

(b) decreases when a body is deformed

(c) remains same when a body is deformed

(d) becomes non-zero when a body is deformed.

4. The nature of molecular forces resembles with the

nature of the

(a) gravitational forces (b) nuclear force

(c) electromagnetic force (d) weak force

5. Elasticity is due to

(a) decreases of PE with separation between

atoms/molecules

(b) increases of PE with separation between

atoms/molecules

(c) asymmetric nature of PE curve


6. For a perfectly rigid body,

(a) Young's modulus is infinite and bulk modulus is zero

(b) Young's modulus is zero and bulk modulus is infinite.

(c) Young's modulus is infinite and bulk modulus is also

infinite

(d) Young's modulus is zero and bulk modulus is also

zero.

7. Statement I Elongation produced in a body is directly

proportional to the applied force.

Statement II This law of elasticity, now called as Hooke’s

law.

(a) Both Statement I and Statement II are correct and

Statement II is the correct explanation of Statement I.

(b) Both Statement I and Statement II are correct but

Statement II is not the correct explanation of Statement I.

(c) Statement I is correct but Statement II is incorrect.

(d) Statement I is incorrect but Statement II is correct.

8. Match the following Column I and Column II

Column I Column II

A. Longitudinal stress 1. Volume changes

B. Shear stress 2. Shape changes

C. Bulk stress 3. Volume does not

change

D. Tensile stress 4. Shape does not

change

A B C D

(a) 1, 4 2,3 1,4 1,4

(b) 2,3 1,4 1,4 1,4

(c) 1 4 1,4 2,3

(d) 2,3 4,1 4 1

9




9. Match the following Column I and Column II. More than

one match are possible.

Column I Column II

A. Young’s modulus of a

substance

1. Depends on

temperature

B. Bulk modulus of a

substance

2. Depends of length

C. Modulus of rigidity of

a substance

3. Depends on area of

cross-section

D. Volume of a

substance

4. Depends on the

nature of material

A B C D

(a) 1,4 1,4 1,4 1,2,3

(b) 1,2 3,2 4,1 1,3,4

(c) 1 3 4 2

(d) 1 4 3 2

10. From the graph, we can see in the region from O to A, the

curve is linear. In this region, Hooke’s law is obeyed.

Thus, from O to A, the solid body behaves as a/an

(a) elastic body (b) partially elastic body

(c) plastic body (d) inelastic body

11. The point B in the curve is known as

(a) yield point (b) elastic limit

(c) plastic limit (d) breaking point

12. Modulus of rigidity of ideal liquid is

(a) infinity

(b) zero

(c) unity

(d) some finite small non-zero constant value

ANSWER KEY

1 B 2 C 3 D 4 C 5 C

6 C 7 A 8 A 9 A 10 A

11 A 12 B

SOLUTION 1. (b) The property of a body, by virtue of which it tends to

region its original size and shape when the applied force

is removed, is known as elasticity and the deformation

caused is known as elastic deformation.

2. (c) Inter-atomic forces are attractive, when atoms are far

from each other and it becomes repulsive when atoms

come very close.

3. (d) When a body is deformed, atoms/ molecules are

displaced from their equilibrium positions (F = 0) and as

a result there is a force (F ≠ 0) acts to restore them.

4. (c) Inter-molecular and inter-atomic forces are due to

electric and magnetic interactions between atoms and

molecules.

5. (c) Elasticity occurs due to asymmetric nature of U versus

graph.

When separation of molecules is less than (or more than)

equilibrium separation, PE of system increases and

system dissipated this energy to reach minimum energy

configuration.

As a result separation is again restored to equilibrium

separation for which U is minimum.

6. (c) For a perfectly rigid body, both young's modulus and

bulk modulus is infinite.

7. (a) Robert Hooke, an English physicist performed

experiments on springs and found that the elongation

(change in the length produced in a body is proportional

to the applied force or load. In 1676, he presented his

law of elasticity, now called Hooke’s law.

8. (a) Longitudinal or tensile stress causes change of length so

volume changes but shape does not change. Shear causes

change of shape Bulk stress causes change of volume.

A → (1,4), B → (2,3), C → (1,4), D → (1,4)

9. (a) A → (1,4), B → (1,4), C → (1,4), D → (1,2,3)

A. Young’s modulus of substance depends on

temperature and nature of material.

B. Bulk modulus of a substance depends on temperature

and nature of material.

C. Modulus of rigidity of a substance depends on

temperature and nature of material.

D. Volume of substance depends on temperature, length

and area of cross-section.

10. (a) In this region, Hooke’s law is obeyed. The body regions

its original dimensions when the applied force is

removed. The solid behave as an elastic body.

11. (a) In the region from A to B, stress and strain are not

proportional. Nevertheless, the b….. still returns to its

original dimension when the load is removed The point

B in the curve is known as yield point (also known as

elastic limit) and the corresponding stress is known as

y) of the material.

12. (b) No viscous force exists in case of ideal fluid, hence

tangential forces are zero so there is no stress develop.

SSC CDS

BANKrAILWAY



Physics



1999 to till date

C L A S S E S

Chapter - 20

(Relativity)

1




THEORY OF RELATIVITY By Albert Einstein in 1915

When speed of object approaches the speed of light (c). Its M, L, T(mass, length, time) shows a different behavior.

Einstein mass energy relation

E = mc2

Etotal energy =KE + Rest mass energy

mc2 = (r – 1) moc2 + moc2

KE = mc2 – moc2 r = 2 2

1

1 v / c

KE = (m – mo)c2

i.e. Decrease in mass is converted into kinetic energy(KE).

Relation between TE(total energy), Rest mass energy & momentum

E2 = p2c2 + 2 4

om c

Decrease in mass converted to kinetic energy

m = o

2 2

m

1 c

mo rest mass of body.

m mass of body movingwith velocity n comparable to speed of light(c)

Length Contraction

L = O 2 2

1L

1 v / c

c speed of light

v velocity of object

LO length in stationary frame

L length in moving frame (moving with velocity c)

2




Time Dilation

t = o

2 2

t

1 v / c

t actual time that appears to stationary man on earth

to time of clock in moving object.

Note: Earth is not an inertial frame because of its orbital and rotational motion but for most of the purposes, earth may be

regarded as an inertial frame of Reference.

A frame of reference consists of an abstract coordinate system and the set of physical reference points that uniquely fix

the coordinate system and standardize measurements

Types of Frame of Reference

Inertial/unaccelerated System

Newton's 1st law holds.

Non-Inertial/Accelerated System

Newton's 1st law does not holds.

Transformations

These are used to convert variables from one frame of reference to another frame of reference.

Transformations

Galileon Transformation if v < c

t' = t

Lorentz Transformation if v >> c

Due to invariance of speed of light in all inertial frames

t' t

v- speed of an object moving in inertial frame

c – speed of light

t- time period

t'- observed time period in another frame of reference

In a Lorentz Transformation, A circle appears to be an ellipse in a frame f' which is moving with velocity v relative to

frame f.

Postulates of Special Theory of Relativity

1. All fundamental laws of physics retain the same form in all the inertial frames of reference.

2. The velocity of light in free space is constant and is independent of relative motion of source and observer.

Michelson-Morley Exp.

Purpose: To confirm the existence of luminiferous ether as stationary.

OR

To find velocity of earth with respect to ether.

3




physics - neon classes · 2020. 9. 10. · 4 manisha bansal ma'am (director & author) 10...

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