chapter 03 - thermal physics

8/9/2019 Chapter 03 - Thermal Physics

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CHAPTER3

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was knighted by King George III o England, and made a

Count in 1791 by Teodor in his brie reign as elector o

the Holy Roman Empire.

In 1793, Tompson lef England ultimately to take up a post

with the beore mentioned Teodor, elector o Bavaria. He

was appointed a major general in the Bavarian army. Hedesigned ortications and worked as an administrator

in munitions. It was here that he observed that a large

amount o heat was generated in the boring o cannons.

He read the ollowing extracts beore the Royal Society o

London in 1798.

Being engaged, lately, in superintending the boring

o cannon, in the workshops o the military arsenal at

Munich, I was struck with the very considerable degree o

Heat which a brass gun acquires, in a short time, in being

bored; and with the still more intense Heat (much greater

than that o boiling water as I ound by experiment) o the

metallic chips separated rom it by the borer.

From whence comes the Heat actually produced in the

mechanical operation above mentioned? Is it urnished by

the metallic chips which are separated by the borer rom

the solid mass o metal? I this were the case, then,

according to the modern doctrines o latent heat, and o

caloric, the capacity or Heat o the parts o the metal, so

reduced to chips, ought not only to be changed, but the

change undergone by them should be sufficiently great to

account or all the Heat produced.

Count Rumord was saying that the metal chips should

have undergone some alteration in their properties afer

the production o so much thermal energy. He noted that

some cannon shavings were hot enough to glow, but he

continued:

But no such change had taken place; or I ound, upon

taking equal quantities, by weight, o these chips, and o

thin slips o the same block o metal separated by means

o a ne saw, and putting them, at the same temperature

(that o boiling water), into equal quantities o cold water,

the portion o water into which the chips were put was

not, to all appearance, heated either less or more than the

other portion, into which the slips o metal were put. Fromwhence it is evident that the Heat produced [by boring the

cannon] could not possibly be urnished at the expense o

the latent Heat o the metallic chips.

Rumord urther went on to explain that he had immersed

cannons in water while they were being bored and noted

the rate at which the temperature rose. His results showed

that the cannon would have melted had it not been cooled.

Rumord concluded that heat was not a caloric uid in

which caloric is conserved but rather a concept o motion.

He argued that heat is generated when work is done, and

that the heat will continue to be generated as long as work

is done. He estimated a heat to work ratio within the order

o magnitude accepted today.

However, many scientists o the time were not convincedbecause Rumord could not give a clear explanation o

exactly what heat was in terms o the accepted model or

matter at that time. It would take another hal century

beore Joule supplied the accepted answers.

JAMES PRESCOTT JOULE

James Prescott Joule (1818-1889) conducted a series o

brilliant experiments between 1842 and 1870 that proved

beyond doubt that heat was a type o energy internal

energy o the particles o matter. Te caloric theory lost

popularity very quickly.

Joulewas the son o a wealthy brewer in Manchester, UK.

Because o his wealth, he never worked or a living. His

experiments were perormed in a laboratory that he built

at his own expense while he was in his twenties. He became

interested in ways to develop more efficient engines that

were driving various components o the brewing process.

Encouraged by the work o Count Rumford and others,

he began to investigate whether mechanical work could

produce heat.

Jouleperormed a variety o experiments and he rened

and elaborated his apparatus and his techniques. In one

o his rst experiments, he used a alling weight to drive

a small electric generator. Te current produced heated a

wire that was immersed in a denite mass o water, and

the change in temperature was noted. He reasoned that

the work done as the weight decreases its gravitational

potential energy should be equivalent to the heat energy

gained by the water. In another experiment he mounted a

large container lled with air into a tub o water. When the

air was compressed, the temperature o the gas increased.

He measured the amount o work needed to compress the

gas and the amount o heat energy given to the water as a

result o compression.

Perhaps Joules most amous experiment consisted o a

paddlewheel mounted inside a cylinder o water that was

driven by alling weights as shown in Figure 301. He wanted

to see i one could raise the temperature o the water simply

by turning the paddles. He repeated this experiment many

times continually improving the apparatus and rening

his analysis o the data. For example, he took great care

to insulate the container so that no heat was lost to the

surroundings, and he developed his own thermometer so

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THERMALPHYSICS

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that he could measure the temperature with a precision o

a raction o a degree.

moving vanes

xed vanes

calorimeter

ywheel

handles

to pulley withweights attached

to pulley withweights

(containing water)

spindle

attached

Figure 301 Schematic diagram of

Joules paddlewheel experiment.

Joule arranged the vanes o the paddlewheel so that they

would not interere with the particles o water set in

motion. He didnt want to bruise or damage the water

particles so that they might bleed heat.

In 1849 he published his results in which he reported

the quantity o heat produced by riction o bodies,

whether solid or liquid, is always proportional to the

quantity o [energy] expended.

the quantity o heat capable o increasing the

temperature o a pound o water by 1 Fahrenheit requires

or its evolution the expenditure o a mechanical energy

represented by the all o 772 pound through the distance

o one oot.

Joule ound that about 4.2 joules o work would yield one

calorie o heat or that the quantity o heat required to

raise the temperature o one gram o water by 1 C is one

calorie.

A modern day value or the mechanical equivalent o heat

is 4.18605 joules = 1 calorie.

Te experiments proved beyond doubt that mechanical

work can produce heat and as such no caloric uid can

be created or destroyed. Furthermore, Joule reasoned that

the temperature increase must be related to the energy o

the microscopic motions o the particles.

Finally, a paradigm shif in our way o reasoning had again

proved that science is not the ultimate truth.

Example

Calculate the mechanical equivalent o heat or Joules

paddlewheel experiment i a mass o 2.0 kg alls through a

height o 100 m, and increases the temperature o 10 g owater by 46.8 C.

Solution

Work done by the alling mass is given by

W = Ep = mgh

= 2.0 kg 9.8 m s -2 100 m

= 1.96 10 3J

Heat energy produced is given by

Q= m c T

= 10 g 1 cal 46.8 C

= 4.68 102calories

Mechanical equivalent o heat is given by

W

Q-----

1.96 103

J

4.68 102 cal----------------------------------=

= 4.19 J cal-1

Te mechanical equivalent o heat or water is 4.2 J cal -1.



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3.1.1 State that temperature determines the

direction of thermal energy transfer

between two objects.

3.1.2 State the relation between the Kelvin and

Celsius scales of temperature.

3.1.3 State that the internal energy of a

substance is the total potential energy and

random kinetic energy of the molecules of

the substance.

3.1.4 Explain and distinguish between the

macroscopic concepts of temperature,

internal energy and thermal energy (heat).

3.1.5 Define the mole and molar mass.

3.1.6 Define theAvogadro constant. IBO 2007

3.1.1 TEMPERATUREANDTHERMAL

ENERGYTRANSFER

Everyone seems to have a feel for the concept of heat

because there is so much talk in everyday conversation

of how hot or how cold it is. We endure the seasons of

the year wanting either to cool our bodies or heat up our

surroundings. We are aware of how difficult it was for

our ancestors to keep warm, and our present dwellings

are designed and insulated to suit the climate. Our

consumption of electrical and chemical energy for heating

and other purposes is a continual concern. We have

become aware that increased global warming could spell

the end of the world, as we know it.

But what is the difference between heat and temperature

in physics? Tey are denitely not the same physical

quantity. If you ll a cup and a dish with hot water at the

same temperature, and then place ice cubes into each, thedish full of hot water can melt more ice cubes than the

cup of hot water even though the water in each was at the

same temperature. Te dish containing the larger amount

of hot water has a greater mass of water as well as a greater

amount of heat or thermal energy. A greater mass infers

a greater number of water molecules and more thermal

energy infers that these molecules would have a greater

overall amount of energy. We cannot see the interaction

of the water molecules at the microscopic level because

we cannot see atoms. However, we can observe and

monitor the temperature change by using a macroscopic

temperature-measuring device.

Termal energyis a measure of the kinetic and potential

energy of the component particles of an object and is

measured in joules. Heat is the thermal energy that is

absorbed, given up or transferred from one object to

another.

emperatureis a scalar quantity that gives an indication of

the degree of hotness or coldness of a body. Alternatively,

temperature is a macroscopic property that measures

the average kinetic energy of particles on a dened scale

such as the Celsius or Kelvin scales. Te chosen scale

determines the direction of thermal energy transferbetween two bodies in contact from the body at higher

temperature to that of lower temperature. Eventually,

the two bodies will be in thermal equilibrium when they

acquire the same temperature in an isolated system. It will

be deduced later in this text that thermal energy cannot

be transferred from a body at lower temperature to that of

higher temperature.

3.1.2 TEMPERATURESCALES

Tere is no instrument that directly measures the amount of

thermal energy a body gives off or absorbs. A property that

varies with temperature is called a thermometricproperty.

Tis property can be used to establish a temperature scale

and construct a thermometer. Termometers are made

using the thermometric properties of a substance such as the

expansion of a liquid, the electrical resistance of a wire.

A typical laboratory thermometer as shown in Figure 302

contains a liquid such as mercury or coloured alcohol. Te

expansion of alcohol is six times greater than mercury.

Alcohol thermometers are safer and can be used at lower

temperatures than mercury which turns to a solid below

-38.9 C. Its disadvantage is that it boils above 78.5 C. o

make the thermometer sensitive, it has a narrow bore tubeand a large bulb. Te bulb is made of thin glass so that

heat can be transferred quickly between the bulb liquid

and the material being observed. Tere is a vacuum above

the thermometer liquid and it can move easily along the

glass bore.

3.1 THERMAL CONCEPTS



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THERMALPHYSICS

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100C

0 C

mercury or alcoholthin glassbulb

glassstem

capil lary tube

vacuum

Figure 302 Typical laboratory thermometer

A clinical thermometer as shown in Figure 303 does not

need the temperature range o a laboratory thermometer.

It is designed so that the maximum temperature remains

constant afer the patients temperature is taken. It has a

small constriction to stop the mercury owing back into

the bulb. Te mercury is then shaken back into the bulb

afer the temperature has been taken.

35 36 37 38 39 40 41 42

Figure 303 A Clinical Thermometer

In order to calibrate these thermometers, two xed points

are used to dene the standard temperature interval. Te

ice point (the lower xed point) marked at 0 C is the

temperature o pure ice at standard atmospheric pressure

and is in thermal equilibrium with the liquid in the bulb.

Te steam point (the upper xed point) marked at 100 C

is the temperature o steam at standard atmospheric

pressure and is in thermal equilibrium with the liquid in

the bulb. Te scale between these values is marked with

even spaces. Te Celsius temperature scale named afer

the Swedish astronomer Anders Celsius (1701-1774) isconstructed in such a manner.

Although thermometers constructed using thermometric

properties are useul or everyday use, they are not

accurate enough or scientic work. Unortunately, two

thermometers constructed using different thermometric

properties do not necessarily agree with each other as they

do not vary linearly over large temperature ranges. (Tey

are o course in agreement at the lower and upper xed

points). For example, different thermometers will give

different values or the boiling point o zinc (907 C).

Te standard undamental temperature scale in the SI

system is denoted by the symbol T. and is measured in

Kelvin, K. It is the thermodynamic temperature scale used

in scientic measurement.

Te lower xed point is absolute zero and is assigned a

value o 0 K. Tis is the point where molecular vibrations

become a minimum the molecules have minimum

kinetic energy but molecular motion does not cease. Te

upper xed point is the triple point o water. Tis is the

temperature at which saturated water vapour, pure water

and melting ice are all in equilibrium. For historical

reasons, it is assigned a value o 273.16 K.

Tin K = T in C + 273.16

Exercise 3.1 (a)

1. At room temperature, an iron rod eels cooler

when held in the hand than wood held in the samewood held in the same

hand. Tis is because:

A. thermal energy tends to ow rom the

metal to the wood

B. wood has a higher specic heat capacity

than the iron rod

C. wood has a lower specic heat capacity than

the iron rod

D. the iron rod conducts thermal energy better

than the wood

2. Explain the difference between heat and

temperature.

3. I you were travelling to Antarctica, deduce

what would be the better thermometer to take

mercury or alcohol?

4. State one advantage and one disadvantage o a

i. mercury in glass thermometer

ii. constant volume thermometer.

5. Te triple point o water is 273.16 K. Express this

as a Celsius temperature.

6. Determine the ice point and the steam point o

pure water on the Kelvin scale?



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7. Dene absolute zero.

8. If normal body temperature is 37.0 C, what is it

on the thermodynamic temperature scale?

3.1.3 HEATANDINTERNALENERGY

Termal energy of a system is referred to as internal energy

- the sum total of the potential energy and the random

kinetic energy of the molecules of the substance making

up the system.

Te potential energy is due to

the energy stored in bonds called bond energy

intermolecular forces of attraction between particles.

Te bond energy is a form of chemical potential energy. It

becomes signicant in chemistry when a chemical reaction

occurs, and bonds are broken and formed.

Te intermolecular forces of attraction between particles

is due to the electromagnetic fundamental force since the

gravitational force is too small to be of any signicance.

Figure 304 indicates how the intermolecular electro-

magnetic forceFbetween particles varies with the distance

rbetween their centres.

At distances greater than r0 (less than 2.5 10-10 m)

attraction takes place, and at distances closer than r0the

particles repel. At r0

the particles are in equilibrium. Any

displacement from the equilibrium position results in a

simple harmonic oscillation of a particle or molecule.

r 0

repulsion

attraction

solid and liquid phase

10r0

gaseous phase

nuclear separation, r / m

Force, F / N

+

Figure 304 Force versus separation of particles

Figure 305 shows the relationship between the potential

energy and the separation rof two molecules. At 0 K, the

average separation of particles centres is r0and the overall

force is zero. Tis is the point of minimum potential

energy. Work will need to be done to move the particles

apart and there will be an increase in potential energy.

r0

equil ibrium separationgas

liquid

separation, r / m

Pote

ntialenergy,

U

/J

solid

+

minimum potentialenergy =

Figure 305 Potential energy

versus separation of particles

Work done = force distance = F r = change in

potential energy

F=E

p

____

r

In other words, the gradient of the potential energy curve

at any point on the curve gives the force that must be

applied to hold the molecules at that separation. We can

classify the phases according to the sizes of the energy .

When less than

__

10

, the vibrations occur about xed

positions and the particles are in the solid phase. When

approximately equal to

__

10

, the particles have sufficient

energy to partly overcome the attractive forces and melting

occurs.

When greater than __10

, a liquid can form. When greater

than , the particles have sufficient energy to leave the

liquid and form a gas.

Te kinetic energy is mainly due to the translational,

rotational and vibrational motion of the particles as

depicted in Figure 306.

Vibrationalki netic energy

Rotationalki netic energy

Translationalki netic energy

Figure 306 major particle motion and energy



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3.1.4 MACROSCOPICCONCEPTSOF

TEMPERATURE

Internal energy and thermal

energy (heat)

A macroscopic property is one that can be observed.

Physical properties such as melting point, boiling point,

density, thermal conductivity, thermal expansion and

electrical conductivity can be observed and measured.

TEMPERATURE

At the macroscopic level, temperature is the degree

of hotness or coldness of a body as measured by a

thermometer. Termometers are made using the

thermometric properties of a substance such as:

the expansion of a column of liquid in a capillary

tube (laboratory and clinical thermometers).

the electrical resistance of a wire (resistance and

thermister thermometers).

the difference in the rates of expansion of two

metals in contact (bimetallic strips).

the pressure of a gas at constant volume.

the volume of a gas at constant pressure (gases

expand by a greater amount and more evenly than

liquids).

the heating of two metal wires wound together

(thermocouple thermometers rely on the two

metals producing different currents).

the colour of a solid heated to high temperatures

(pyrometers).

emperature is measured in Kelvin, K.

INTERNAL ENERGY

As already mentioned, internal energyis the sum total of

the potential energy and the random kinetic energy of the

molecules of the substance making up a system. In order

to apply the Law of conservation to thermal systems, onehas to assume that a system has internal energy.

At the macroscopic level, it can be observed that molecules

are moving. When pollen (a ne powder produced by

owers) is sprinkled on the surface of water and the set-

up is viewed under magnication, it can be seen that the

pollen particles carry out zig-zag motion called Brownian

Motion.Teir motion is caused by the kinetic energy of

the water molecules. Walking past a coffee shop you smell

the aroma of the coffee due to diffusion caused by the

kinetic energy of the air molecules allowing the aroma

molecules to spread.

Te expansion of solids, liquids and gases is a macroscopic

property that allows us to understand that matter in a

system has potential energy. When you heat a liquid it canbe seen to expand as in a thermometer and this means

that the potential energy of the system is increasing as

the molecules move further apart. Te compressibility of

gases allow us to understand that the potential energy of

the molecules is decreasing.

Although the internal energy in the examples above can

never be absolutely determined, the change in internal

energy can be observed.

THERMAL ENERGY HEAT

Students should understand that the term thermalenergy refers to the non-mechanical transfer of energy

between a system and its surroundings. IBO 2007

Terefore, it is incorrect to refer to the thermal energy in a

body. At the macroscopic level, thermal energy (heat) can

be transferred from one body to another by conduction,

convection, radiation or by combinations of these three.

Termal conductionis the process by which a temperature

difference causes the transfer of thermal energy from the

hotter region of the body to the colder region by particle

collision without there being any net movement of the

substance itself.

Termal convectionis the process in which a temperature

difference causes the mass movement of uid particles

from areas of high thermal energy to areas of low thermal

energy (the colder region).

Termal radiationis energy produced by a source because

of its temperature that travels as electromagnetic waves. It

does not need the presence of matter for its transfer.

Conduction can occur in solids, liquids and gases. Ingases it occurs due to the collision between fast and slow

moving particles where kinetic energy is transferred

from the fast to the slow particle. Te transfer of energy

is very slow because the particles are far apart relative

to solids and liquids. In liquids, a particle at higher

temperature vibrates about its position with increased

vibrational energy. Because the majority of the particles

are coupled to other particles they also begin to vibrate

more energetically. Tese in turn cause further particles



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CORE

to vibrate and thermal conduction occurs. Tis process is

also slow because the particles have a large relative mass

and the increase in vibrations is rather small. In solids, the

transfer can occur in one of two ways. Most solids behave

similarly to liquids.

However, solids are held in their xed positions morerigidly than liquids and the transfer of vibrational energy

is more effective. However, again their large masses do not

allow for large energy transfer. If a substance in the solid

or molten form has mobile electrons, as is the case for

metals, these electrons gain energy due to the temperature

rise and their speeds increase much more than those held

in their xed positions in the lattice. Metals are said to be

good conductors of heat but most other solids are good

insulators. Saucepans for cooking are usually made of

copper or aluminium because these metals conduct heat

quickly when placed on a stove. Te handle is made from

a good solid insulator to reduce the conduction of heat.

Generally, liquids and gases are not good thermal

conductors. However, they can transfer heat readily by

convection. Ocean currents, wind and weather patterns

suggest that the mass movement of particles from one area

to another can cause movement of particles on the grand

scale.

Figure 307 shows a potassium permanganate crystal placed

in water inside a convection tube. Heat is applied for a

short period of time and the direction of the purple trail

is noted. Particles in a region of high thermal energy are

further apart and hence their density is lower. In a region

of low thermal energy the particles are closer together and

the region is more dense. As a result, the less dense region

rises as it is pushed out of the way by the more dense

region and a convection current is produced.

Heat

Potassium

permanganatecrystal

water

Convection tube

Figure 307 Convection current.

Another way in which a uid can move is by forced

convection. In this case, a pump or fan system maintains

the movement of a uid. Te cooling system in nuclear

reactors operates on this principle.

All thermal energy ultimately comes from the Sun in our

solar system. It travels through 150 million km of mostly

empty space. At the Earths atmosphere the radiant energy

is mainly reected back into space. However, some is

transmitted and absorbed causing a heating effect. Just as

the Sun emits thermal radiation so does any source that

produces heat such as a light bulb or an electric heater.Termal radiation is mainly electromagnetic waves in

the infra-red region of the electromagnetic spectrum at

temperatures below 1000 C. Above this temperature,

wavelengths of the visible and ultra-violet regions are

also detected. Dull black bodies are better absorbers and

radiators than transparent or shiny bodies.

3.1.5,6 THE MOLE,

MOLAR MASS AND

AVOGADROS NUMBERTe mass of an atom is exceedingly small. For example,the mass of a uorine atom is 3.16 10-23g and the mass of

the isotope carbon12 is 1.99 10-23 g. Because the masses

of atoms are so small, it is more convenient to describe

the mass of an atom by comparing its mass with those of

other atoms.

In 1961 the International Union of Pure and Applied

Chemistry (IUPAC) dened the masses of atoms relative to

carbon12 that was assigned a value of 12.0000. Terefore,

the relative atomic mass is dened as the mass of an atom

when compared with 1/12 the mass of carbon12 atom.

Just as the relative atomic mass is used to describe the

masses of atoms, the relative molecular mass is used to

describe the masses of molecules. Terefore, the relative

molecular mass is dened as the mass of a molecule when

compared with 1/12 of the mass of a carbon12 atom.

It is convenient to group things into quantities. For

example, a box of diskettes, a ream of photocopy paper

(500 sheets), a dozen eggs are common groupings. Te

SI fundamental unit for the amount of a substance is the

mole(mol).

Te mole is the amount of substance that contains asmany elementary particles as there are in 0.012 kg of

carbon12.

Amadeo Avogadro(1776 1856) found that equal volumes

of gases at the same temperature and pressure contained

the same number of particles. One mole of any gas contains

the Avogadro numberof particles NA. It is now known

that one mole of a gas occupies 22.4 dm3 at 0 C and



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THERMALPHYSICS

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101.3 kPa pressure (SP) and contains 6.02 1023

particles.

When using the mole, the atoms or molecules should be

clearly stipulated. For example, one mole of copper atoms

contains 6.02 1023copper atoms. One mole of nitrogen

molecules (N2) contains 6.02 1023

of nitrogen moleculesand 12.04 1023nitrogen atoms.

If we have one mole of NH4NO

3, this contains:

1 mol of NH4

+ions = 6.02 1023ammonium ions

1 mol of NO3

ions = 6.02 1023nitrate ions

2 mol of nitrogen atoms = 1.204 1024nitrogen atoms

4 mol of hydrogen atoms = 2.408 10 24hydrogen atoms

3 mol of oxygen atoms = 1.806 1024oxygen atoms

Te amount of substance (the moles) is related to the mass

and the molar mass according to the following equation:

n = m__M

where

n= amount of a substance in mol, m= the mass in g and

M= the molar mass in g mol -1. Te molar mass can be

obtained from the periodic table.

Example

1. Calculate the number of moles of oxygen

molecules contained in 64.0 g of oxygen gas, O2.

2. Calculate the number of oxygen molecules in part

1 of this example.

3. Determine the volume of oxygen gas that would

be present at SP.

4. Calculate the mass in 0.75 mol of carbon dioxide gas.

Solution

1. n = m__M

=64.0 g

_________________

(

16.0 + 16.0)g mol1= 2 mol

2. Te number of oxygen molecules

= 2NA

the number of molecules

= 6.02 1023 2

= 1.024 1024 molecules.

3. Volume

= 2 mol 22.4 dm3

= 44.8 dm3

4. m = n M

= 0.75 mol (12 +16 +16) g mol-1

= 33 g



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CORE

Exercise 3.1 (b)

1. Te internal energy of a substance is equal to:

A. the total potential energy stored in thebonds of a substance

B. the potential and kinetic energy of

molecules in a substance

C. the energy stored in bonds and

intermolecular forces of a substance

D. the translational, rotational and vibrational

motion of particles in the substance

2. Te number of moles of sodium chloride (NaCl)

in 100g of pure sodium chloride is (Mrof NaCl =

58.5 gmol-1)

A. 5850 molB. 0.585 mol

C. 1.71 mol

D. 41.5 mol

3. wo different objects with different temperatures

are in thermal contact with one another. When the

objects reach thermal equilibrium, the direction of

transfer of thermal energy will be

A. from the lower temperature object to the

higher temperature object

B. half way between the temperatures of the

two objects

C. from the higher temperature object to the

lower temperature object

D. in many different directions

4. A sealed ask contains 16 g of oxygen (mass

number 16) and also 8 g of hydrogen (mass

number 1). Te ratio of the number atoms of

hydrogen to the number of atoms of oxygen is

A. 16

B. 8

C. 4D. 2

5. Te number of molecules present in 0.5 mol SO3is

A. 3 1023

B. 6 1023

C. 12 1023

D. 24 1023

6. Te number of atoms present in 0.5 mol SO3is

A. 3 1023

B. 6 1023

C. 12 1023

D. 24 1023

7. Calculate the approximate molar masses of each of

the following molecules and compounds:

(a) Cl2

(b) HCl

(c) CuSO4

(d) Na2CO

3

(e) CH4

8. Calculate the mass of the given amounts of each of

the following substances:

(a) 2.0 mole of iron, Fe(b) 0.2 mole of zinc, Zn

(c) 2.5 mole of carbon dioxide, CO2

(d) 0.001 mole of sulfur dioxide, SO2

(e) 50 mole of benzene, C6H

6

9. Calculate the amount of subtance (number of

mole) in:

(a) 100 g of copper

(b) 5.0 g of oxygen molecules

(c) 100 g of calcium carbonate, CaCO3

(d) 4.4 g of carbon dioxide

(e) 13.88 g of lithium

10. A sample of aluminium sulfate Al2(SO

4)

3has a

mass of 34.2 g. Calculate:

(a) the number of alumimium ions Al3+in the

sample

(b) the number of sulfate ions SO4

2-in the

sample

11. Classify the following as a macroscopic or

microscopic property of a gas

(a) volume

(b) specic heat capacity

(c) kinetic energy of a particle

(d) pressure

(e) temperature



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3.2.1 Define specific heat capacityand thermal

capacity.

3.2.2 Solve problems involving specific heat

capacities and thermal capacities.

3.2.3 Explain the physical dierences between

the solid, liquid and gaseous phases in

terms of molecular structure and particle

motion.

3.2.4 Describe and explain the process of phase

changes in terms of molecular behaviour.

3.2.5 Explain in terms of molecular behaviour

why temperature does not change during aphase change.

3.2.6 Distinguish between evaporation and

boiling.

3.2.7 Define specific latent heat.

3.2.8 Solve problems involving specific latent

heats. IBO 2007

3.2.1 THERMALCAPACITY

When different substances undergo the same temperature

change they can store or release different amounts of

thermal energy. Tey have different thermal (heat)

capacities. If a substance has a high heat capacity it will

take in the thermal energy at a slower rate than a substance

with a low heat capacity because it needs more time to

absorb a greater quantity of thermal energy. Tey also

cool more slowly because they give out thermal energy at

a slower rate.

We dene the thermal (heat) capacity as,

Termal Capacity =Q

___

T J K -1

Qis the change in thermal energy in joules J

Tis the change in temperature in kelvin degrees K.

Water is used in car cooling systems and heating systems

because of its high thermal capacity. A metal heat sink is

used on the back of refrigerators because of its low thermal

capacity.

Example

Te thermal capacity of a sphere of lead is 3.2 103 JK-1

Determine how much heat can be released if the

temperature changes from 61C to 25C.

Solution

Q T apacity= Thermal c

3.2 103JK

1 61 25( ) C=

3.2 103

JK1

36 C

115200J

1.2 105

J

Note that a change in Kelvin temperature is the

same as a change in Celsius temperature

3.2.2 SPECIFICHEATCAPACITY

Heat capacity does not take into account the fact that

different masses of the same substance can absorb or

release different amounts of thermal energy.

Consider three one kilogram blocks of aluminium, zinc

and lead with the same sized base that have been heated

to the same temperature of 80 C. Tey are quickly placed

on top of a large block of candle wax for a time period as

shown in Figure 308.

Figure 308 Front-on view of the

metal blocks after a period of time.

3.2 THERMAL PROPERTIES OF MATTER

C A N D L E WAX

Aluminium Zinc Lead



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Te aluminium block melts the most wax and the lead

melts the least. Tereore, the metals o the same mass

give out different amounts o thermal energy in a certain

time period. Tis can be explained rom a microscopic

viewpoint. Te kilogram unit masses have different

numbers o particles o different types and masses. Te

metal blocks were given the same amount o thermalenergy when they were heated to 80 C. When the thermal

energy gained by each metal is distributed amongst its

particles, the average energy change o each particle will

be different or each metal.

o obtain a characteristic value or the heat capacity

o materials, equal masses o the materials must be

considered. Te physical property that includes the mass

is called the specific heat capacity o a substance c.

Specic heat capacityor specific heat is the heat capacity

per unit mass. It is defined as the quantity o thermal

energy required to raise the temperature o a unit mass oa substance by one degree Kelvin.

c=Q

_____

m

Q= m c

Q= the change in thermal energy required to produce a

temperature change in Joules, J.

m= mass o the material in grams (g) kilograms (kg)

= the temperature change in Kelvin, K.

Note that is always positive because heat always

transers rom the higher temperature region to the lower

temperature region.

For gases, the molar heat capacity at constant volume Cv

and the molar heat capacity at constant pressure Cp are

more commonly used. Molar heat capacity is the quantity

o heat required to raise the temperature o one mole o the

gas by one degree Kelvin under the constant condition.

Figure 309 shows the specific heat capacity or some

common substances at room temperature (except ice)

Substance Specic heatJ kg -1K -1 Substance Specic heatJ kg -1K -1

Lead 1.3 102 Iron 4.7 102

Mercury 1.4 102 Aluminium 9.1 102

Zinc 3.8 102 Sodium 1.23 103

Brass 3.8 102 Ice 2.1 103

Copper 3.85 102 Water 4.18 103

Figure 309 Specific heat of some common substances

Example

Determine how much thermal energy is released when

650 g o aluminium is cooled rom 80 C to 20 C.

Solution

Using the fact that Q = m.c., we have,

Q = 0.650 kg 9.1 102J kg-1K-1 (80 20) K

= 3.549 104J

= 4 104J

Tat is, 4 104J of heat is released.

Example

An active solar heater is used to heat 50 kg o water initially

at a temperature o 12 C. I the average rate that thermal

energy is absorbed in a one hour period is 920 J min -1 ,

determine the equilibrium temperature afer one hour

Solution

Quantity of heat absorbed in one hour = 920 J min -1

60 min = 5.52 104J

Using the fact that Q = m c , we have

5.52 104J = 5.0 101kg 4.18 103J kg-1K-1 (f 12)K

5.52 104J = 2.09 105JK-1 (f 12) C

5.52 104J = 2.09 105f 2.51 106J

2.09 105f= 5.52 104J + 2.51 106J

f=

2.553 106J

______________

2.09 105(J K1)

f= 12.26 C

f= 12 C



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THERMALPHYSICS

85

EXTENSION METHODS TO DETERMINE

SPECIFIC HEAT CAPACITY

A calorimeter is a useul piece o equipment or

investigations in Termal Physics because it allows masses

at different temperatures to be mixed with minimum

energy loss to the surroundings. It is used or direct andindirect methods in determining the specific heat capacity

o a substance. (Te name o the instrument is derived

rom the Imperial unit, the calorie.)

copper vessel

heating coil

liquid

thermometer

stirrer

lagging

joulemeter

Figure 310 Calorimeter being used to measure the

heating effect of a current

Figure 310 illustrates the use o a calorimeter to determine

the specific heat capacity o a liquid, in this case water.

Te heating coil is used to convert electrical energy to

thermal energy. Te electrical energy can be measured by

a joulemeter or by using a voltmeter/ammeter circuit. Te

duration o time o electrical input is noted.

Te thermal energy gained by the calorimeter cup and the

water is equal to the electrical energy lost to the calorimeter

cup and water.

Electrical energy lost =

V I t = [m c T]calorimeter cup

+ [m c T]water

where Vis the potential difference across the heating coil

in volts V and Iis the current in the amperes, A.

Te specific heat capacity, c, o the calorimeter cup isobtained rom published values. Te other quantities are

recorded and the specific heat capacity o the water is

calculated.

In calorimeter investigations, heat losses to the

surroundings need to be minimised. It is normal to polish

the calorimeter cup to reduce loss o heat due to radiation.

Te calorimeter is also insulated with lagging materials

such as wool or polystyrene to reduce heat loss due to

conduction and convection.

Afer the power supply is switched off, the temperature

should continue to rise or a period, and then level out or

an infinite time. However, heat is lost to the surroundings,

and the maximum temperature that could be achieved,in theory, is never reached. Instead appreciable cooling

occurs. One method used to estimate the theoretical

maximum temperature is to use a cooling correction

curveas shown in Figure 311.

{Note that cooling correction is not required in the syllabus

but is included or possible extended essays.}

t 2t 3t

A1

A2

2

A1

A2------ =

1

3 2 +=

3

, so that

2

1=( )

(= correction)

Temperatur

e,

C

Time, minutes

actual curve

theoreticalcurve

roomtemp

Figure 311 Graph of cooling correction.

A cooling correction is based on Newtons Law o Cooling.

It states that the rate o loss o heat o a body is proportional

to the difference in temperature between the body and its

surroundings (excess temperature). A ull explanation o

this Law will not be given. I the power supply is switched off

at time 2tminutes, then the temperature should continue

to be recorded or a urther t minutes. Te correction

to the temperature can be obtained rom the graph as

shown. Te final temperature, 3,is then given as the final

temperature o the thermometer plus the correction .

Another direct electrical method used to determine the

specific heat capacity o a metal is shown in Figure 312.

An immersion heater is placed into a metal block. Te

hole or the heater is lubricated with oil to allow evenheat transmission. Te electrical energy lost to the block

is recorded or a given period o time and the specific

heat o the metal is calculated. Cooling correction is more

important in this case because the temperatures under

which the investigation is carried out could be much

higher than was the case when using a calorimeter.

19 april 09 Physics Ch 3 final.i85 85 22/05/2009 11:49:2


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CHAPTER3

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CORE

metal block

thermometer

lagging

V

A

Low voltagesupply

immersionheater

Figure 312 Electrical method using

an immersion heater and a metal block

A common indirect method to determine the specific

heat capacity of a solid and liquids is called the method of

mixtures. In the case of a solid, a known mass of the solid

is heated to a certain temperature, and then transferred

to a known mass of liquid in a calorimeter whose specific

heat capacity is known. Te change in temperature is

recorded and the specific heat of the solid is calculatedfrom the results obtained. In the case of a liquid, a hot

solid of known specific heat is transferred to a liquid of

unknown specific heat capacity.

Example

A block of copper of mass 3.0 kg at a temperature of

90 C is transferred to a calorimeter containing 2.00 kg of

water at 20 C. Te mass of the copper calorimeter cup is

0.210 kg. Determine the final temperature of the water.

Solution

Te thermal energy gained by the water and the calorimeter

cup will be equal to the thermal energy lost by the copper.

Tat is, [mc]copper

= [mc]calorimeter cup

+ [mc]cup

We also have that,

Termal energy lost by the copper

= (3.0 kg) (3.85 102J kg -1K -1) (90.0 f) K

Termal energy gained by the water

= (2.0 kg) (4.18 103J kg -1K -1) (f 20.0) K

Termal energy gained by the cup

= (0.21 kg) (9.1 102J kg -1K -1) (f 20.0) K

1.04 105 1.155 103f

= (8.36 103f 1.67 105) +(1.91 102f 3.82 103)

Tat is,

9.71 103f = 2.75 105

Giving

f = 28.3 C

Te nal temperature of the water is 28 C

Exercise 3.2 (a)

1. Te amount of thermal energy required to raise

the temperature of 1.53 103g of water from 15 K

to 40 K is

A. 1.6 107J

B. 1.6 105J

C. 4.4 107J

D. 4.4 105J

2. Te specific heat capacity of a metal block of mass

mis determined by placing a heating coil in it, as

shown in the following diagram.

Te block is electrically heated for time t and the

maximum temperature change recorded is . Te

constant ammeter and voltmeter readings during

the heating are Iand V respectively. Te electrical

energy supplied is equal to VIt.



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THERMALPHYSICS

87

metal block

thermometer

lagging

V

A

Low voltagesupply

immersionheater

Te specific heat capacity is best calculated using

which one of the following expressions?

A. c=VI

m

B. c=

m

VI

C. c=m

VIt

D. c=VIt

m

3. 5.4 106J of energy is required to heat a 28 kg

mass of steel from 22 C to 450 C. Determine the

specific heat capacity of the steel.

4. Liquid sodium is used as a coolant in some

nuclear reactors. Describe the reason why liquid

sodium is used in preference to water.

5. 6.00 102kg of pyrex glass loses 8.70 106J of

thermal energy. If the temperature of the glass was

initially 95.0 C before cooling, calculate is its final

temperature.

(ake the specific heat capacity of pyrex glass to be

8.40 10 2J kg -1 K-1)

6. A piece of wood placed in the Sun absorbs more

thermal energy than a piece of shiny metal of the

same mass. Explain why the wood feels cooler

than the metal when you touch them.

7. A hot water vessel contains 3.0 dm3 at 45 C.

Calculate the rate that the water is losing thermal

energy (in joules per second) if it cools to 38 C

over an 8.0 h period.

8. Determine how many joules of energy are released

when 870 g of aluminium is cooled from 155 C to

20 C.

9. If 2.93 106J is used to raise the temperature of

water from 288 K to 372 K, calculate the mass of

water present.

10. 1.7 mJ of energy is required to cool a 15 kg mass of

brass from 400 C to 25 C. Determine the specific

heat capacity of brass.

11. A piece of iron is dropped from an aeroplane at

a height of 1.2 km. If 75% of the kinetic energy

of the iron is converted to thermal energy on

impact with the ground, determine the rise in

temperature.

12. If 115 g of water at 75.5 C is mixed with 0.22 kg of

water at 21 C, determine the temperature of the

resulting mixture.

13. Describe an experiment that would allow you to

determine the specific heat capacity of a metal.

(i) Sketch the apparatus.

(ii) Describe what measurements need to be

made and how they are obtained.

(iii) State and explain the equation used to

calculate the specific heat capacity of the

metal.

(iv) Describe 2 main sources of error that are

likely to occur in the experiment.

(v) Is the experimental value likely to be higher

or lower than the theoretical value, if the

experiment was carried out in a school

laboratory? Explain your answer.

14. A heating uid releases 4.2 107 Jkg-1 of heat as it

undergoes combustion. If the uid is used to heat

250 dm3of water from 15 C to 71 C, and the

conversion is 65% efficient, determine the mass

of the heating uid that will be consumed in this

process.

15. A large boulder of 125 kg falls off a cliff of height

122 m into a pool of water containing 120 kg of

water. Determine the rise in temperature of the

water. Assume that no water is lost in the entry ofthe boulder, and that all the heat goes to the water.

16. A thermally insulated container of water is

dropped from a large height and collides

inelastically with the ground. Determine the

height from which it is dropped if the temperature

of the water increases by 1.5 C.



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CHAPTER3

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CORE

17. A piece of copper is dropped from a height of

225 m. If 75% of its kinetic energy is converted to

heat energy on impact with the ground, calculate

the rise in temperature of the copper. (Use the

table of specific heat capacities to find the value for

copper).

18. 5kg of lead shot is poured into a cylindrical

cardboard tube 2.0 m long. Te ends of the tube

are sealed, and the tube is inverted 50 times. Te

temperature of the lead increases by 4.2 C. If

the specific heat of lead is 0.031 kcal kg-1C-1,

determine the number of work units in joules that

are equivalent to the heat unit of 1 kilocalorie.

3.2.3 PHASESTATES

An understanding of thermal energy is based upon a theory

called the moving particle theory or kinetic theory (forgases) that uses models (Figure 314) to explain the structure

and nature of matter. Te basic assumptions of this moving

particle theory relevant to thermal energy are:

all matter is composed of extremely small particles

all particles are in constant motion

if particles collide with neighbouring particles, they

conserve their kinetic energy

a mutual attractive force exists between particles

solid liquid gas

Figure 314 Arrangement of particles

in solids, liquids and gases

An atom is the smallest neutral particle that represents an

element as displayed in a periodic table of elements. Atoms

contain protons, neutrons and electrons and an array of

other sub-atomic particles. Atomic diameters are of the

order of magnitude 1010

m. Atoms can combine to formmolecules of substances. In chemistry, the choice of the

terms e.g. atoms, molecules, ions are specific to elements

and compounds. In physics, the word particle is used to

describe any of these specific chemistry terms at this stage

of the course.

As previously mentioned, evidence for the constant motion

of particles can be gained from observation of what is

known as Brownian Motion. If pollen grains from owers

are placed on water and observed under a microscope, the

pollen grains undergo constant random zig-zag motion.

Te motion becomes more vigorous as the thermal energy

is increased with heating. A Whitley Bay smoke cell uses

smoke in air to achieve the same brownian motion. In both

cases, the motion is due to the smaller particles striking

the larger particles and causing them to move.

Te large number of particles in a volume of a solid, liquid

or gas ensures that the number of particles moving in all

directions with a certain velocity is constant over time.

Tere would be no gaseous state if the particles were losing

kinetic energy.

A mutual attractive force must exist between particles

otherwise the particles of nature would not be combined

as we know them. Further explanation of this assumption

will be given later in this topic.

Matter is defined as anything that has mass and occupiesspace. Tere are four states of matter which are also called

the four phases of matter solids, liquids, gases and

plasma. Most matter on Earth is in the form of solids,

liquids and gases, but most matter in the Universe is in the

plasma state. Liquids, gases and plasma are uids.

A plasma is made by heating gaseous atoms and molecules

to a sufficient temperature to cause them to ionise. Te

resulting plasma consists then of some neutral particles but

mostly positive ions and electrons or other negative ions.

Te Sun and other stars are mainly composed of plasma.

Te remainder of this chapter will concentrate on the other

three states of matter, and their behaviour will be explained in

terms of their macroscopic and microscopic characteristics

of which some are given in Figures 315 and 316.

Characteristic Solid Liquid Gas

Shape Definite Variable Variable

Volume Definite Definite Variable

CompressibilityAlmost

Incompressible

Very slightly

Compressible

Highly

Compressible

Diffusion Small Slow Fast

Comparative

Density High High Low

Figure 315 Some macroscopic

characteristics of solids, liquids and gases

Macroscopic properties are all the observable behaviours of

that material such as shape, volume and compressibility.



17/26

THERMALPHYSICS

89

Te many macroscopic or physical properties of a substance

can provide evidence for the nature and structure of that

substance.

Characteristic Solid Liquid Gas

Kinetic energy Vibrational

Vibrational

Rotational

Some

translational

Mostly

translationalHigher

rotational

Higher

vibrational

Potential energy High Higher Highest

Mean molecular

Separation (r0)

r0

r0

10r0

Termal energy

of particles ()< /10 < > /10 >

Molecules per m3 1028 1028 1025

Figure 316 Some microscopiccharacteristics of solids, liquids and gases

Microscopic characteristics help to explain what is

happening at the atomic level, and this part of the model

will be interpreted further at a later stage.

Te modern technique of X-ray diffraction that will be

studied in detail in a later chapter has enabled scientists

to determine the arrangement of particles in solids. Te

particles are closely packed and each particle is strongly

bonded to its neighbour and is held fairly rigidly in a fixed

position to give it definite shape in a crystalline lattice.

Some patterns are disordered as is the case for ceramics,

rubber, plastics and glass. Tese substances are said to be

amorphous. Te particles have vibrational kinetic energy

in their fixed positions and the force of attraction between

the particles gives them potential energy.

In liquids the particles are still closely packed and the

bonding between particles is still quite strong. However,

they are not held as rigidly in position and the bonds can

break and reform. Tis infers that the particles can slowly

and randomly move relative to each other to produce

variable shape and slow diffusion. Particles in a liquid

have vibrational, rotational and some translational kineticenergy due to their higher mean speeds. Te potential

energy of the particles in a liquid is somewhat higher than

for a solid because the spacing between the particles is

large.

In gasesthe particles are widely spaced and the particles

only interact significantly on collision or very close

approach. Because of the rapid random zig-zag motion of

the particles, a gas will become dispersed throughout any

container into which it is placed. Diffusion (the spreading

out from the point of release) can occur readily. Gases

are compressible because the particles are widely spaced

at a distance much greater than the size of the particles.

Te much higher mean speeds are due to an increased

translational kinetic energy of the particles. Gases have

a much higher potential energy than liquids because theparticles are much further apart.

3.2.4 THEPROCESSOFPHASE

CHANGES

A substance can undergo changes of state or phase changes

at different temperatures. Pure substances (elements and

compounds) have definite melting and boiling points

which are characteristic of the particular pure substance

being examined. For example, oxygen has a melting point

of -218.8 C and a boiling point of -183 C at standard

atmospheric pressure.

Te heating curve for benzene is illustrated in Figure 317.

A sample of benzene at 0C is heated in a closed container

and the change in temperature is graphed as a function

of time. Te macroscopic behaviour of benzene can be

described using the graph and the microscopic behaviour

can be interpreted from the macroscopic behaviour.

SO L I D

L I QU ID

G AS

L iquid-gas phasechange

Solid-liquidphase change

Temperature /C

H eating time /min

meltingpoint

boilingpoint

5.5C

80C

Figure 317 Heating curve for benzene.

When the solid benzene is heated the temperature

begins to rise. When the temperature reaches 5.5 C the

benzene begins to melt. Although heating continues the

temperature of the solid liquid benzene mixture remains

constant until all the benzene has melted. Once all thebenzene has melted the temperature starts to rise until the

liquid benzene begins to boil at a temperature of 80 C.

With continued heating the temperature remains constant

until all the liquid benzene has been converted to the

gaseous state. Te temperature then continues to rise as

the gas is in a closed container.



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CORE

3.2.5 MOLECULARBEHAVIOURAND

PHASECHANGES

he moving particle theory can be used to explain the

microscopic behaviour o these phase changes. Whensolid benzene is heated the particles o the solid vibrate

at an increasing rate as the temperature is increased.

he vibrational kinetic energy o the particles increases.

At the melting point a temperature is reached at which

the particles vibrate with suicient thermal energy to

break rom their ixed positions and begin to slip over

each other. As the solid continues to melt, more and

more particles gain suicient energy to overcome the

orces between particles and over time all the solid

particles change to a liquid. he potential energy o

the system increases as the particles begin to move. As

heating continues the temperature o the liquid rises

due to an increase in the vibrational, rotational andpart translational kinetic energy o the particles. At

the boiling point a temperature is reached at which the

particles gain suicient energy to overcome the inter-

particle orces present in the liquid benzene and escape

into the gaseous state. Continued heating at the boiling

point provides the potential energy needed or all the

benzene molecules to be converted rom a liquid to a

gas. With urther heating the temperature increases

due to an increase in the kinetic energy o the gaseous

molecules due to the larger translational motion.

3.2.6 EVAPORATIONANDBOILING

When water is lef in a container outside, exposed to the

atmosphere, it will eventually evaporate. Mercury rom

broken thermometers has to be cleaned up immediately

due to its harmul effects. Water has a boiling point o

100 C and mercury has a boiling point o 357 C. Yet they

both evaporate at room temperature.

Te process o evaporation is a change rom the liquid

state to the gaseous state that occurs at a temperature

below the boiling point.

Te moving particle theory can be applied to understandthe evaporation process. A substance at a particular

temperature has a range o kinetic energies. So in a liquid

at any particular instant, a small raction o the molecules

will have kinetic energies considerably greater then the

average value. I these particles are near the surace o the

liquid, they may have enough kinetic energy to overcome

the attractive orces o neighbouring particles and escape

rom the liquid as a vapour. Now that the more energetic

particles have escaped, the average kinetic energy o the

remaining particles in the liquid has been lowered. Since

temperature is proportional to the average kinetic energy

o the particles, a lower kinetic energy implies a lower

temperature, and this is the reason why the temperature o

the liquid alls as evaporative coolingtakes place. Another

way o explaining the temperature drop is in terms o latent

heat. As a substance evaporates, it needs thermal energyinput to replace its lost latent heat o vaporisation and this

thermal energy can be obtained rom the remaining liquid

and its surroundings.

A substance that evaporates rapidly is said to be a volatile

liquid. A liquids volatility is controlled by a actor known

as its equilibrium vapour pressure. Tere are orces that

must be overcome beore a particle can leave the surace o

a liquid. Different liquids exert different vapour pressures

that depend on the relative strengths o the intermolecular

orces present in the liquids. Hydrouorocarbons and

CFCs used in rerigerators, and ether, chloroorm and

ethanol have relatively high vapour pressures.

Te values in Figure 318 compare the vapour pressure o

some liquids at 293 K.

Substance Vapour pressure / kPa

Ether 58.9

Chloroorm 19.3

Ethanol 5.8

Water 2.3

Mercury 0.0002

Figure 318 Some common vapour pressures

Although the vapour pressure o mercury is much lower

than the other substances listed at room temperature,

some evaporation does occur. Because o its extreme

toxicity any mercury spill is treated seriously. Ether has a

high vapour pressure. I a stream o air is blown through a

sample o ether in a beaker that is placed on a thin film o

water, the water will eventually turn to ice.

When overheating occurs in a human on hot days, the

body starts to perspire. Evaporation o the perspiration

results in a loss o thermal energy rom the body so thatbody temperature can be controlled. Local anaesthetics

with high vapour pressures are used to reduce pain on the

skin. Termal energy ows rom the surrounding esh

causing its temperature to drop and thereby anaesthetises

the area.

A liquid boils when the vapour pressure o the liquid

equals the atmospheric pressure o its surroundings.

As the boiling point is reached, tiny bubbles appear



19/26

THERMALPHYSICS

91

throughout the liquid. I the vapour pressure o the bubble

is less than the atmospheric pressure the bubbles are

crushed. However a point is reached when the pressures

are equal. Te bubble will then increase in size as it rises to

the surace o the liquid.

Exercise 3.2 (b)

1. When smoke is strongly illuminated and viewed

under a microscope it is possible to observe

A. all particles moving in straight lines

B. smoke particles moving randomly by air

molecules

C. smoke particles colliding with each other

D. air molecules in random motion

2. Te internal energy o a monatomic gas such asneon is mainly due to

A. the potential energy holding the atoms in

fixed positions

B. the vibrational energy o the atoms

C. the random translational energy o the

atoms

D. the rotational energy o the atoms

3. For a given mass o a certain liquid, the magnitude

o the thermal energy transer is the same or the

ollowing two processes

A. reezing and sublimation

B. melting and evaporation

C. evaporation and condensation

D. sublimation and condensation

4. Which o the ollowing is a unit o thermal

energy?

A. watt

B. the product o the newton and the metre

C. the quotient o the watt and the second

D. the product o the joule and the second

Base your answers to Questions 5 and 6 on the ollowing

graph. Te graph shows the temperature o an unknown

substance o mass 10.0 kg as heat is added at a constant

rate o 6300 Jmin-1. Te substance is a solid at 0 0C.

Time / min

0 5 10 15 20

Temperature/oC

150

100

50

5. Te internal potential energy o the unknown

substance increases without any change in internal

kinetic energy rom the beginning o the:

A. first minute to the end o the ourth minute

B. seventh minute to the end o the

seventeenth minuteC. seventeenth minute to the end o the twenty

first minute

D. nineteenth to the end o the twenty fifh

minute

6. Te specific heat capacity o the substance when it

is solid is:

A. 63 Jkg-1K-1

B. 105 Jkg-1K-1

C. 126 Jkg-1K-1

D. 504 Jkg-1K-1

7. Give five macroscopic and five microscopic

characteristics o the liquid/gas in a butane lighter.

8. Describe the components o internal energy in

each o the ollowing situations

(a) air at room temperature

(b) a jar o honey

(c) a melting ice cream.

9. Explain the difference between heat, thermal

energy and temperature.

10. Does a block o ice contain any heat? Explain your

answer ully.

11. Draw a ully labelled cooling curve or the

situation when steam at 110 C is converted to ice

at 25 C.



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CHAPTER3

92

CORE

12. (a) Convert 63 C to Kelvin

(b) Convert 52 K to degrees Celsius

13. Te temperatures o the same volume o air and

water are raised by a small amount. Explain why

a different amount o heat is required or each

process.

14. I you increase the heat under a pot o water in

which you are boiling potatoes, will the potatoes

be cooked aster?

15. I you wanted to cool a bottle o sof drink at the

beach, would you be better to wrap a wet towel

around it or to put it into the seawater? Explain

your answer.

16. Why is it important not to stand in a draught afer

vigorous exercise?

17. Describe and explain the process o evaporative

cooling in terms o its microscopic properties.

18. A kettle made o stainless steel containing water

is heated to a temperature o 95 C. Describe

the processes o thermal energy transer that are

occurring in the stainless steel kettle and the water.

3.2.7 LATENTHEAT

Te thermal energy which a particle absorbs in melting,

evaporating or sublimating or gives out in reezing,

condensing or sublimating is called latent heat because it

does not produce a change in temperature. See Figure 320.

T H E R M A L E N E R G Y A D DE D

melting evaporation

SO L ID L IQUID G A S

freezing condensation

sublimation

T H E R M A L E N E R G Y GIV E N OU T

Figure 320 Macroscopic

transformations between states of matter.

Sublimation is a change o phase directly rom a solid to

a gas or directly rom a gas to a solid. Iodine and solid

carbon dioxide are examples o substances that sublime.

When thermal energy is absorbed/released by a body,

the temperature may rise/all, or it can remain constant.

I the temperature remains constant then a phase change

will occur as the thermal energy must either increase the

potential energy o the particles as they move urther

apart or decrease the potential energy o the particles as

they move closer together. I the temperature changes,then the energy must increase the average kinetic energy

o the particles.

Te quantity o heat required to change one kilogram o

a substance rom one phase to another is called thelatent

heat of transformation.

Q = mL

Qis the quantity o heat absorbed or released during the

phase change in J,

mis the mass o the substance in kg and

Lis the latent heat o the substance in J kg -1

Lcould be the latent heat o usion L, the latent heat o

vaporisation Lvor the latent heat o sublimation L

s. Te

latent heat o usion o a substance is less than the latent

heat o vaporisation or the latent heat o sublimation. More

work has to be done to reorganise the particles as they

increase their volume in vaporisation and sublimation

than the work required to allow particles to move rom

their fixed position and slide over each other in usion.

Figure 321 lists the latent heat o some substances.

Substance Melting

point

K

Latent heat

of fusion

105 J kg-1

Boiling

point

K

Latent heat of

Vaporisation

105J kg-1

Oxygen 55 0.14 90 2.1

Ethanol 159 1.05 351 8.7

Lead 600 0.25 1893 7.3

Copper 1356 1.8 2573 73

Water 273 3.34 373 22.5

Figure 321 Some Latent Heat Values

Example

Calculate the heat energy required to evaporate 5.0 kg o

ethanol at its boiling point.



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THERMALPHYSICS

93

Solution

Given that m = 5.0 kg and Lv= 8.7 105J kg -1.

We then have,

= 4.35 106J = 4.4 106J

Te heat energy required for the vaporisation is 4.4 106J.

Example

Determine the heat energy released when 1.5 kg of

gaseous water at 100 C is placed in a freezer and

converted to ice at -7 0C. Te specific heat capacity of ice

is 2.1 103J kg1 K1..

Solution

Te energy changes in this process can be represented as

shown in Figure 322.

Using

Q = mLV+ mc

WAER+ mL

f+ mc

ICE

= m [LV+ c

WAER+ L

f+ c

ICE]

= 1.5 [22.5 105+ (4180 100) + 3.34 105+ (2100 7)]

= 4.52 106J

Tat is, the energy released is 4.5 106J or 4.5 MJ.

T H E R M A L E N E R G Y R E L E A SE D

I C E at L IQUID water at GASE OUS water at

7C 0 C 0 C 100 C 100 C

L atent heat of fusion L atent heat of evaporation

Specic heatI ce Specic heat water

Figure 322 Energy released in steam-ice change.

Te latent heat of vaporisation can be found using a self-

jacketing vaporiser as shown in Figure 323. Te liquid

to be vaporised is heated electrically so that it boils at a

steady rate. Te vapour that is produced passes to the

condenser through holes labelled H in the neck of the

inner ask. Condensation occurs in the outer ask and

the condenser.

A

C old water

C ondenser

Water outow

Liquid underinvestigation

Heating coil

Vapour acting asa jack et

C ollecting vessel

C ondensed vapour

V

H H

Figure 323 Latent heat of vaporisation apparatus.

Eventually, the temperature of all the parts of the apparatus

becomes steady. When this steady state is reached, a

container of known mass is placed under the condenser

outlet for a measured time t, and the measured mass of the

condensed vapour mis determined. Te heater current I

is measured with the ammeter A and potential difference

V is measured with a voltmeter V. Tey are closely

monitored and kept constant with a rheostat.

Te electrical energy supplied is used to vaporise the liquid

and some thermal energy His lost to the surroundings.

Terefore:

V1I

1t= m

1L

V+ H

In order to eliminate Hfrom the relationship, the process

is repeated using a different heater potential difference

and current. Te vapour is collected for the same time t

Te rate of vaporisation will be different but the heat lost

to the surroundings will be the same as each part of the



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CHAPTER3

94

CORE

apparatus will be at the same temperature as it was with

the initial rate vaporisation.

Terefore:

V2I

2t= m

2L

V+ H

By subtracting the two equations:

(V1I

1 V

2I

2)t= (m

1 m

2)L

V

From this equation, the value of the latent heat

of vaporisation of the unknown substance can be

determined.

Exercise 3.2 (c)

1. Te specific latent heat of fusion of ice is the heatrequired to

A. raise the temperature of ice from 0 C to 10 C

B. change 1 dm3of ice at 0 C to water at 0 C

C. change 1kg of ice at 0 C to water at 0 C

D. change the temperature of 1 kg by 10 C

2. A substance changes from liquid to gas at its

normal boiling temperature. What change, if

any, occurs in the average kinetic energy and the

average potential energy of its molecules?

Average kinetic Average potential

energy energy

A. constant increases

B. increases constant

C. increases decreases

D. constant constant

3. Termal energy is transferred to a mass of water

in four steps. Which one of the four steps requires

the most thermal energy?

A. 5 C to 20 CB. 15 C to 35 C

C. 75 C to 90 C

D. 95 C to 101 C

4. Determine the amount of thermal energy that is

required to melt 35 kg of ice at its melting point.

5. A 5.0 102g aluminium block is heated to 350 C.

Determine the number of kilograms of ice at 0 C

that the aluminium block will melt as it cools.

6. Steam coming from a kettle will give you a nastier

burn than boiling water. Explain why.

7. An immersion heater can supply heat at a rate of

5.2 102J s -1. Calculate the time that it will take

to completely evaporate 1.25 10-1kg of water

initially at a temperature of 21 C?

8. A 3.45 kg sample of iron is heated to a temperature

of 295 C and is then transferred to a 2.0 kg copper

vessel containing 10.0 kg of a liquid at an initial

temperature of 21.0 C. If the final temperature of

the mixture is 31.5 C, determine the specific heatcapacity of the liquid?

9. A mass of dry steam at 1.0 102C is blown over

a 1.5 kg of ice at 0.0 C in an isolated container.

Calculate the mass of steam needed to convert the

ice to water at 21.5 C.

10. A freezer in a refrigerator takes 2.00 hours to

convert 2.15 kg of water initially at 21.5 C to just

frozen ice. Calculate the rate at which the freezer

absorbs heat.

11. Describe an experiment to determine the specific

heat capacity of an unknown metal. Sketch the

apparatus used and describe what measurements

are made. State the main sources of error and

explain how they can be minimised.

12. Calculate how much thermal energy is released

when 1.2 kg of steam at 100 C is condensed to

water at the same temperature.

(Lv= 2.25 106Jkg-1)

13. Determine how much energy is released when

1.5 kg of gaseous water at 100 C is placed in afreezer and converted to ice at 7 C . (the specific

heat capacity of ice is 2.1 103J kg-1 K-1).

14. Describe an experiment that can be used to

determine the latent heat of vaporisation of a

liquid.



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THERMALPHYSICS

95

KINETIC MODEL OF AN IDEAL GAS

3.2.9 Define pressure.

3.2.10 State the assumptions of the kinetic model

Of an ideal gas.

3.2.11 State that temperature is a measure of

the average random kinetic energy of the

molecules of an ideal gas.

3.2.12 Explain the macroscopic behaviour of an

ideal gas in terms of a molecular model. IBO 2007

3.2.9 PRESSURE

Investigations into the behaviour of gases involve

measurement of pressure, volume, temperature and mass.Experiments use these macroscopic properties of a gas to

formulate a number of gas laws.

In 1643 orricelli found that the atmosphere could

support a vertical column of mercury about 76 cm high

and the first mercury barometer became the standard

instrument for measuring pressure. Te pressure unit

760 mm Hg (760 millimetres of mercury) represented

standard atmospheric pressure. In 1646, Pascal found that

the atmosphere could support a vertical column of water

about 10.4 m high.

For our purposes in this section, pressurecan be defined

as the force exerted over an area.

Pressure = Force / Area

P = F /A

Te SI unit of pressure is the pascal Pa.

1 atm = 1.01 105Nm-2= 101.3 kPa = 760 mmHg

3.2.10 THEKINETICMODELOFAN

IDEALGAS

An ideal gas is a theoretical gas that obeys the ideal gas

equation exactly. Real gases conform to the gas laws under

certain limited conditions but they can condense to liquids,

then solidify if the temperature is lowered. Furthermore,

there are relatively small forces of attraction between

particles of a real gas, and even this is not allowable for

an ideal gas.

Most gases, at temperatures well above their boiling pointsand pressures that are not too high, behave like an ideal gas.

In other words, real gases vary from ideal gas behaviour at

high pressures and low temperatures.

When the moving particle theory is applied to gases it is

generally called the kinetic theory of gases. Te kinetic

theory relates the macroscopic behaviour of an ideal gas to

the behaviour of its molecules.

Te assumptions or postulates of the moving particle

theory are extended for an ideal gas to include

Gases consist of tiny particles called atoms(monatomic gases such as neon andargon) or

molecules.

Te total number of molecules in any sample of a

gas is extremely large.

Te molecules are in constant random motion.

Te range of the intermolecular forces is small

compared to the averageseparation of the

molecules.

Te size of the particles is relatively small compared

with the distance between them.

Collisions of short duration occur between

molecules and the walls of the container and the

collisions are perfectly elastic.

No forces act between particles except when they

collide, and hence particlesmove in straight lines.

Between collisions the molecules obey Newtons

Laws of motion.

Based on these postulates the view of an ideal gas is one

of molecules moving in random straight line paths at

constant speeds until they collide with the sides of the

container or with one another. Teir paths over time are

therefore zig-zags. Because the gas molecules can move

freely and are relatively far apart, they occupy the total

volume of a container.

Te large number of particles ensures that the number of

particles moving in all directions is constant at any time.



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CHAPTER3

96

CORE

3.2.11 TEMPERATUREANDAVERAGE

RANDOMKINETICENERGY

Temperature is a measure of the average random kinetic

energy of an ideal gas.

At the microscopic level, temperature is regarded

as the measure o the average kinetic energy per

molecule associated with its movements. For gases,

it can be shown that the average kinetic energy,

Ek1

2---mv2

3

2---kT= = where k= Boltzmann constant

v2 T

Te term average kinetic energy is used because, at a

particular temperature different particles have a wide

range o velocities, especially when they are converted to agas. Tis is to say that at any given temperature the average

speed is definite but the velocities o particular molecules

can change as a result o collision.

Figure 325 shows a series o graphs or the same gas

at three different temperatures. In 1859 James Clerk

Maxwell (1831-1879) and in 1861 Ludwig Boltzmann

(1844-1906) developed the mathematics o the kinetic

theory o gases. Te curve is called a Maxwell-Boltzmann

speed distribution and it is calculated using statistical

mechanics. It shows the relationship between the relative

number o particles N in a sample o gas and the speeds v

that the particles have when the temperature is changed.

(T3> T

2> T

1)

Te graphs do not show a normal distribution as the

graphs are not bell-shaped. Tey are slightly skewed to

the lef. Te minimum speed is zero at the lef end o

the graphs. At the right end they do not touch the x-axis

because a small number o particles have very high speeds.

Te peak o each curve is at the most probable speed vp

a large number o particles in a sample o gas have their

speeds in this region. When the mathematics o statistical

mechanics is applied it is ound that mean squared speed

vav

2 is higher than the most probable speed. Another

quantity more ofen used is called the root mean square

speed Vrmsand it is equal to the square root o the meansquared speed.

vrms v2

=

Te root mean square is higher than the mean squared

speed.

Other eatures o the graphs show that the higher the

temperature, the more symmetric the curves becomes.

Te average speed o the particles increases and the peak

is lowered and shifed to the right. Te areas under the

graphs only have significance when N is defined in a

different way rom above.

Figure 326 shows the distribution o the number o

particles with a particular energy N against the kinetic

energy o the particles Ekat a particular temperature. Te

shape o the kinetic energy distribution curve is similar to

the speed distribution curve and the total energy o the

gas is given by the area under the curve.

T1

T2

T2 T1>

N

Ek

Figure 326 Distribution of kinetic energies

for the same gas at different temperatures.

Te average kinetic energy o the particles o all gases is

the same. However, gases have different masses. Hydrogen

molecules have about one-sixteenth the mass o oxygenmolecules and thereore have higher speeds i the average

kinetic energy o the hydrogen and the oxygen are the same.

Because the collisions are perectly elastic there is no loss

in kinetic energy as a result o the collisions.

Figure 325 Maxwell-Boltzmann speed distribution for

the same gas at different temperatures.

vmpv vrms

T1

T2

T3

T3 T2 T1> >

N

vms 1



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THERMALPHYSICS

97

3.2.12 MACROSCOPICBEHAVIOUROF

ANIDEALGAS

Robert Boyle (1627-1691) discussed that the pressure of a

gas at constant temperature is proportional to its density.He also investigated how the pressure is related to the

volume for a fixed mass of gas at constant temperature.

Boyles Law relates pressure and volume for a gas at fixed

temperature.

Boyles Law for gases states that the pressure of a fixed mass

of gas is inversely proportional to its volume at constant

temperature.

P 1__V

PV= constant

When the conditions are changed, with the temperature

still constant

P1V

1= P

2V

2

Te readings of Pand Vmust be taken slowly to maintain

constant temperature because when air is compressed, it

warms up slightly.

When a pressure versus volume graph is drawn for the

collected data a hyperbola shape is obtained, and when

pressure is plotted against the reciprocal of volume a

straight line (direct proportionality) is obtained. See

Figure 327.

pressure, Pmm H g pr ess ure, P mm Hg PV

volume, V cm3

1V

cm3 P

Figure 327 (a), (b) and)c) pressure-volume graphs.

Te pressure that the molecules exert is due to theircollisions with the sides of the container. When the

volume of the container is decreased, the frequency of the

particle collisions with the walls of the container increases.

Tis means that there is a greater force in a smaller area

leading to an increase in pressure. Te pressure increase

has nothing to do with the collisions of the particles with

each other.

In 1787 Jacques Charles (17461823) performed

experiments to investigate how the volume of a gas

changed with temperature. Gay-Lussac (17781850)

published more accurate investigations in 1802.

A very simple apparatus to investigate Charles Law is

shown in Figure 328. A sample of dry air is trapped in acapillary tube by a bead of concentrated sulfuric acid. Te

capillary tube is heated in a water bath and the water is

constantly stirred to ensure that the whole air column is at

the same temperature.

thermometer

water bath

bead of acid(e.g. sulfuric acid)

air column

capillary tube

H E A T

Figure 328 Apparatu

chapter 03 - thermal physics

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