chapter 12 thermal properties of materials

CAMBRIDGE A LEVEL

PHYSICS

MATERIALS

THERMAL

PROPERTIES OF

MATERIALS

L EA R N I N G O U TC O M E SL EA R N I N G O U TC O M E SNo. LEARNING OUTCOME

i Use simple kinetic model to explain the structure of solids, liquids and gases.

ii Relate internal energy to the average potential energies and average kinetic

energies. Relate changes in temperature with changes in internal energy.

iii Use the simple kinetic model to explain why boiling and melting occurs

without any change in temperature and why liquids cool when evaporation

occurs.

iv Define specific latent heat (of fusion and vaporisation) and specific heat

capacity. Explain electrical methods to determine the specific latent heat and

specific heat capacity. Compare specific latent heats of fusion and

vaporisation.

v Relate the work done by/on a gas to its internal energy.

vi Relate changes of state with change in internal energy. Differentiate systems

from surroundings.

vii Define and use the first law of thermodynamics

The kinetic model of matter assumes that all The kinetic model of matter assumes that allmatter is made up of molecules thatinteract with each other and are a state ofcontinuous , random motion.

Evidence: Brownian motion.

We will now compare the structure of 3phases of matter (solids, liquids and gases) interms of ordering, movement andintermolecular distances.

SIMPLE KINETIC MODEL

P R O P E R T I E S O F PA R T I C L E S

PROPERTY SOLIDS LIQUIDS GASES

Ordering of

molecules

Regular structures

repeated

throughout (long

range order ).

Regular ordering

only in the

immediate

neighbourhood of a

few molecules (short

range order).

No ordering.


Figures 21.2 (a) , (b), and (c), page 328, Chapter 21: Thermal Physics; Cambridge

International AS and A Level Physics Coursebook, Sang, Jones, Chadha and Woodside,

2nd edition, Cambridge University Press, Cambridge, UK,2014.

P R O P E R T I E S O F PA R T I C L E S

PROPERTY SOLIDS LIQUIDS GASES

Movement Free to vibrate

about a fixed

position

Can vibrate and

translate due to

some empty spaces

Free to undergo

translational

motion.

Distance

between

molecules

Least amount of

spacing of the

three phases.

Only slightly more

spaced that in solid

of the same

substance

Widely separated.


INTERNAL ENERGY

Each molecule in a substance has a

certain amount of energy.

This energy is the sum of its kinetic

energy; due to its movement, and the

potential energy; due to the interaction

between the molecules.

INTERNAL ENERGY

The amount of potential energy each

molecule has depends on the spacing

between the molecules.

The closer the molecules are, the more

negative (larger) the potential energy.

Potential energy is assigned a negative

sign.

INTERNAL ENERGY

This is seen in the graph below.

Figures 21.5, page 329, Chapter 21: Thermal Physics; Cambridge International AS and

A Level Physics Coursebook, Sang, Jones, Chadha and Woodside, 2nd edition,

Cambridge University Press, Cambridge, UK,2014.

INTERNAL ENERGYThis means that solid molecules have the This means that solid molecules have themost negative (largest) stored potentialenergy, followed by liquid molecules.

Gas molecules store an insignificant amountof potential energy.

However, the difference in stored potentialenergies between solid and liquid moleculesis lower compared to between liquid andgas molecules.

INTERNAL ENERGY

All the molecules will have different

kinetic energies as some are moving

faster and some slower.

All the molecules also will have different

amount of potential energies the

separation between molecules change

continually.

INTERNAL ENERGY

We can now say that the kinetic energies

and potential energies of all of the

molecules follow a random distribution.

When we add the kinetic energies and

potential energies of all the molecules,

we remove the random nature of the

energies.

INTERNAL ENERGY

What we get is known as the internal

energy of the substance.

Definition: The internal energy of a

substance is the sum of the random

distribution of kinetic and potential energies

of all the molecules associated with the

system.

C H A N G E S I N I N T E R N A L E N E R G Y C H A N G E S I N I N T E R N A L E N E R G Y

A N D T E M P E R AT U R E

How do temperature and internal energy of

a substance are related?

When the internal energy of a substance

changes, in certain cases, the temperature

of the substance also changes.

However, if the temperature of a substance

changes, the internal energy of that

substance will change.

For example, when we heat a liquid from 20 For example, when we heat a liquid from 20C to 80 C, the temperature increasesbecause the supplied thermal energyincreases the average kinetic energy of themolecules of the liquid (but not thepotential energy).

When cooling, say from 80 C to 20 C,thermal energy is dissipated since theaverage kinetic energy of the moleculesdecreases.



However, when water boils, the supplied

thermal energy increases the potential

energy of the water molecules, but not

the average kinetic energy (no increase

in temperature).



In conclusion, only changes in average

kinetic energy of the molecules will change

the temperature of the substance. This

happens when matter is heated.

During change of phase, no change in

temperature occurs as the added thermal

energy is used to change the potential

energy stored in the molecules.



I N T E R N A L E N E R G Y A N D

I D E A L G A S E S

I N T E R N A L E N E R G Y A N D

I D E A L G A S E S

molecules.

Recall that for ideal gases, there are no

forces that exist between the gas

molecules. This means that ideal gas

molecules do not store potential energy.

Hence, the internal energy of an ideal

gas equals it sum of the random

distribution of kinetic energies of all its

molecules.

M E LT I N G , B O I L I N G A N D

E VA P O R AT I O N


E VA P O R AT I O N

We will now answer these two

questions:

1. Why melting and boiling occur at a

constant temperature for a specific

substance?

2. Why liquids that undergo evaporation

cool?


E VA P O R AT I O N


E VA P O R AT I O N

Question 1:

Melting and boiling involve change of phase.

During melting, the phase of a substance

changes from solid into liquid at a constant

temperature.

During boiling, the phase change that occurs

is from liquid into gas, also without any

change in temperature.


E VA P O R AT I O N


E VA P O R AT I O N

In solids, the stored potential energy in In solids, the stored potential energy inmolecules is more negative (greater inmagnitude) as compared to that in liquidsbecause the separation between solidmolecules is lesser than that between liquidmolecules.

In order to liquefy, the molecules need tobe separated more. (i.e. the potential energymade more positive).


E VA P O R AT I O N


E VA P O R AT I O N

During melting, the thermal energy

supplied is used to increase the

separation between molecules without

increasing the average kinetic energy of

the molecules. Hence, solids melt

without any increase in temperature.


E VA P O R AT I O N


E VA P O R AT I O N

In liquids, the stored potential energy in In liquids, the stored potential energy inthe molecules is more negative (greaterin magnitude) as compared to that ingases due to the lesser separationbetween molecules in liquids.

In order to boil, the liquid moleculesneed to separated further (i.e. thepotential energy made more positive).


E VA P O R AT I O N


E VA P O R AT I O N

During boiling, the thermal energy

supplied is used to increase the

separation between molecules without

increasing the average kinetic energy of

the molecules. Hence, liquids boil

without any increase in temperature.


E VA P O R AT I O N


E VA P O R AT I O N

kinetic energy of the liquid.

Question 2:

During evaporation, the fastest moving

molecules , i.e. the molecules with the

greatest kinetic energies on the surface

of the liquid undergo a change in phase

(into gas).

This causes a reduction in the average

kinetic energy of the liquid.


E VA P O R AT I O N


E VA P O R AT I O N

A reduction in the average kinetic energy

would reduce the temperature of the

liquid because the average kinetic energy

is proportional to the temperature of the

liquid.

S P EC I F I C H EAT C A PAC I T Y

Definition: Specific heat capacity is the

amount of thermal energy needed to cause a

unit temperature change per unit mass of a

substance without any change in phase.

How do we determine the specific heat

capacity of a substance? Refer to the next 3

slides.


Box 21.1, pages 337, Chapter 21:

Thermal Physics; Cambridge

International AS and A Level

Physics Coursebook, Sang, Jones,

Chadha and Woodside, 2nd edition,

Cambridge University Press,

Cambridge, UK,2014.

EXAMPLEEXAMPLEWorked Example and Figure

21.14, page 337, Chapter 21:

Thermal Physics; Cambridge

International AS and A Level

Physics Coursebook, Sang,

Jones, Chadha and Woodside,

2nd edition, Cambridge

University Press, Cambridge,

UK,2014.

SPECIF IC LATENT HEAT

Definition: Specific latent heat is the amount

of thermal energy needed to cause phase

change to occur in per unit mass of a

substance without any change in

temperature.

Note: Specific refers to per unit of mass.

How do we determine the specific latent heat

of a substance? Refer to the next 2 slides.


Box 21.2, pages 339 and 340, Chapter 21: Thermal Physics; Cambridge International

AS and A Level Physics Coursebook, Sang, Jones, Chadha and Woodside, 2nd edition,

Cambridge University Press, Cambridge, UK,2014.

T Y P E S O F L AT E N T H EAT

There are two kinds of latent heat; latent heat

of fusion and latent heat of vaporisation.

Fusion is the phase change that occurs when a

liquid undergoes phase change to become

solid. Fusion is the opposite of melting.

Vaporisation is the phase change that occurs

when a liquid undergoes phase change into

gas. Vaporisation is opposite to condensation.

E X A M P L E S

Worked Example 3, page 339, Chapter 21: Thermal Physics; Cambridge

International AS and A Level Physics Coursebook, Sang, Jones, Chadha and

Woodside, 2nd edition, Cambridge University Press, Cambridge, UK,2014.

The data in the table compares the

specific latent heats of fusion and

vaporisation. You will observe that the

specific latent heats of vaporisation will

be higher than the specific latent heats

of fusion for all the substances given?

Why is this so?

C O M PA R I N G L AT E N T H E AT S O F

F U S I O N W I T H VA P O R I S AT I O N







Source: http://www.kshitij-school.com/Study-Material/Class-11/Physics/Heat-and-

first-law-of-thermodynamics/Latent-heat/2.jpg

the same substance.

When a unit mass of a substance changes

phase from a liquid to gas, it undergoes a

greater increase in volume as compared to

when a solid changes into a liquid.

This means that the required amount of

change of average potential energy per unit

mass during the vaporisation process is much

greater than that for the fusion process for

the same substance.





Hence, the required increase in internal

energy per unit mass would be larger in

vaporisation (or condensation) as compared

to melting (or fusion) for the same

substance.

The added thermal energy changes only the

average potential energy of the molecules.





E X A M P L E S

Oct/Nov 2008 Paper 4, Question 2.

E X A M P L E S

Oct/Nov 2008 Paper 4, Question 2 (contd).

W O R K D O N E O N A G A S

Assume we have a frictionless moving piston

that attached to a container that contains gas.

We apply a compressive force as shown below.Figure 21.9 b, page 332, Chapter 21: Thermal

Physics; Cambridge International AS and A Level

Physics Coursebook, Sang, Jones, Chadha and

Woodside, 2nd edition, Cambridge University

Press, Cambridge, UK,2014.


The gas is pushed inwards; i.e. undergoes

compression under constant pressure

conditions as seen below.Figure 19.4(b), page 626: Chapter 19:

THE FIRST LAW OF

THERMODYNAMICS; SEARS AND

ZEMANSKYS UNIVERSITY PHYSICS

WITH MODERN PHYSICS; Young,

Hugh D. and Freedman, Roger A.,

Addison Wesley, San Francisco, 2012.


We are pushing the against the gas; i.e. doing

positive work on the gas.

The molecules that collide with the moving

piston will bounce off faster, thus increasing

the average kinetic energy of the molecules.

This causes the internal energy to increase,

hence the temperature of the gas increases.


How do we calculate this work done on the

gas? Use

o work done on the gas, in J;

o the constant pressure, in Pa;

o = change in volume (amount of compression),

in m3

o = final volume, in m3

o = initial volume, in m3

W O R K D O N E BY A G A S

What happens if the gas pushes outwards; i.e.

undergoes expansion under constant pressure

conditions as seen below?Figure 19.4(a), page 626: Chapter 19:

THE FIRST LAW OF


ZEMANSKYS UNIVERSITY PHYSICS

WITH MODERN PHYSICS; Young,

Hugh D. and Freedman, Roger A.,

Addison Wesley, San Francisco, 2012.


Now, the gas does work on the surroundings;

i.e. work done by gas is negative.

This is because the molecules bounce off

slower, thus reducing the average kinetic

energy of the molecules.

This reduces the internal energy of the

molecules and the temperature of the gas.


How do we calculate this work done by the

gas? We may use

o where work done by the gas, in J;

o the constant pressure, in Pa;

o = change in volume (amount of expansion), in

m3

o = final volume, in m3

o = initial volume, in m3


A N D C H A N G E S I N S TAT E

Recall the state variables: P, V and T.

A change in any one of the state

variables will cause a change in state;

the system moves from one state to

another.

A change in state may cause the internal

energy of the system to change.


A N D C H A N G E S I N S TAT E

Changes in state are path

independent. This means that if we

move from state A to state D directly, or

move from state A to B to C then to D ,

Before we look at the first law of

thermodynamics, it is a good idea

first to understand what is meant by

the term system and its

surroundings.

It is up to us to define the system

(and surroundings).

SYS T E M / S U R R O U N D I N G S


For example, if we have cylinder that is

fitted with a piston that contains an ideal

gas, then:

I. the ideal gas alone could be the system, then

the cylinder and piston and everything else

would be the surroundings;

II. the cylinder, piston and ideal gas can be the

system. In this case everything else will be the

surroundings.

If we have an electrical heater that is

placed in a beaker containing a liquid, the

system could either be:

I. the heater only , in this case the liquid

and the beaker and everything else is the

surroundings; or

II. the heater, the liquid and the beaker; i.e.

everything else is the surrounding.


F I R S T L AW O F

T H E R M O D Y N A M I C S

F I R S T L AW O F


Definition: The first law of thermodynamics

states that the change in the amount of

internal energy of a system is equal to the

sum of the amount of the work done on the

system and the amount of thermal energy

added to the system.

F I R S T L AW O F


F I R S T L AW O F


Mathematically, ; where

the increase in internal energy

of the system;

the thermal energy added to the

system; and

the work done on the system

(by the surroundings).

F I R S T L AW O F


F I R S T L AW O F


What this means is we can change the internal

energy of a system either by:

I. adding to ( or removing from (

thermal energy in a system;

II. The surrounding doing work on a system (,

or the system doing work on the surroundings

();

III. Both I and II above

EXAMPLESEXAMPLESQuestion 3, page

332, Chapter 21:

Thermal Physics;

Cambridge

International AS

and A Level Physics

Coursebook, Sang,

Jones, Chadha and

Woodside, 2nd

edition, Cambridge

University Press,

Cambridge,

UK,2014.

CYCLIC PROCESSES

A cyclic process is a process which returns the

state of a system to its initial state.

Since the system returns to its initial state, the

increase in internal energy of the system is

zero; or .

Thus total thermal energy added to the

system plus the work done on the system; or

.

EXAMPLESEXAMPLES

Example 19.4, page 633: Chapter 19: THE FIRST LAW OF THERMODYNAMICS; SEARS AND

ZEMANSKYS UNIVERSITY PHYSICS WITH MODERN PHYSICS; Young, Hugh D. and Freedman,

Roger A., Addison Wesley, San Francisco, 2012.

EXAMPLESEXAMPLESFigure 19.13, example 19.4, page 633:

Chapter 19: THE FIRST LAW OF


ZEMANSKYS UNIVERSITY PHYSICS WITH

MODERN PHYSICS; Young, Hugh D. and

Freedman, Roger A., Addison Wesley,

San Francisco, 2012.

EXAMPLESEXAMPLESOct/Nov 2010, Paper 41, question 2.

EXAMPLESEXAMPLESOct/Nov 2010, Paper 41, question 2 (contd).

H O M E W O R K

1. Question 3, Paper 4, Summer 2009.1. Question 3, Paper 4, Summer 2009.

2. Question 3, Paper 41, Winter 2009.


4. Question 2, Paper 41, Summer 2010.





H O M E W O R K


10.Question 2, Paper 41, Winter 2012.

11.Question 3, Paper 41, Winter 2012.

chapter 12 thermal properties of materials

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