Section III 13 Thermal Properties of Materials

7/28/2019 Section III 13 Thermal Properties of Materials

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Thermal properties of materials

13. Thermal Properties of Materials Content

13.1 Specific heat capacity

13.2 Specific latent heat

13.3 Internal energy

13.4 First law of thermodynamics

Learning Outcomes

(a) explain using a simple kinetic model for matter why

(i) melting and boiling take place without a change in temperature,

(ii) the specific latent heat of vaporisation is higher than specificlatent heat of fusion for the same substance,

(iii) a cooling effect accompanies evaporation.


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(b) define and use the concept of specific heat capacity, andidentify the main principles of its determination by electricalmethods.

(c) define and use the concept of specific latent heat, andidentify the main principles of its determination by electrical

methods. (d) relate a rise in temperature of a body to an increase in its

internal energy.

(e) show an understanding that internal energy is determined bythe state of the system and that it can be expressed as the sumof a random distribution of kinetic and potential energiesassociated with the molecules of a system.

(f) recall and use the first law of thermodynamics expressed interms of the change in internal energy, the heating of the systemand the work done on the system.


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Thermal properties of materials

Heat is a form of energy associated with temperature. A rise inthe temperature of a body means the body is gaining heat

energy.

It is conveyed in a process of transfer by conduction, convection

or radiation from one body to another due to a temperature

difference between the two bodies. The rise in temperature of a body is a result of an increase in the

energy of the body.

In an ideal gas, temperature is the measure of the average kinetic

energy of the molecules, hence it does not depend on how many

molecules are present in the gas


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Internal Energy of gases, U

The molecules of an ideal gas possess kinetic energy and it isproportional to the thermodynamic temperature of the gas

The sum of the kinetic energies of all the molecules due to theirrandom nature is called the internal energy of the ideal gas

Not all molecules have the same kinetic energy, because they aremoving with different speeds, but the sum of all the kinetic

energies will be constant if the gas is kept at a constanttemperature

For an ideal gas, P.E. is zero and hence U = K.E.

The situation for a real gas is different as the molecules exertforces on each other and at any instant there will be a certainpotential energy associated with the position the moleculesoccupy in space

For a real gas the molecules also collide with each other andhence p.e and k.e are changing all the time

Hence internal energy is the sum of the potential energies and thekinetic energies of the molecules

That is, U = P.E. + K.E.


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Internal Energy of matter, U

The idea of internal energy can be extended to all states of matter In a liquid the intermolecular forces are stronger as the molecules

are closer together, hence the potential energy contribution ismore significant

In a solid the potential energy contributions is caused by thestrong binding forces between atoms and the kinetic energy

contribution is due to the motion of the vibrating atoms The internal energy of a body at a particular temperature is the

inherent energy content associated with the bodys molecularstructure and is the sum of the kinetic energy (orvibrational/translational energy) and the potential energy of thebodys molecules.

The internal energy of a matter in any physical state is actually

the sum of the potential (P.E.) and kinetic (K.E.) energies of theatoms or molecules. The potential energy measures the relativepositions of the atoms or molecules in the chemical structure ofthe matter concerned. The kinetic energy measures thevibrational or translational motion of the atoms or molecules.

That is, U = P.E. + K.E.


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Why the concept of internal energy

Useful as it helps to distinguish between temperature and heat

Temperature is a measure of the average kinetic energy of themolecules and does not depend on the number of moleculespresent

Internal energy is the total energy of the molecules and hencedepends on the number of molecules

Heat refers to the transfer of energy from one substance toanother

eg if 10 g of a liquid at 30 C is placed in contact with 100 g of

the same liquid at 20 C, the direction of heat flow is from theliquid at 30 C to the liquid at 20 C eventhough the liquid at 20C has a greater internal energy than the smaller mass of liquidat 30 C


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Specific Heat Capacity, c

The specific heat capacity of a substance is the quantityof heat required to raise the temperature of 1 kg of thesubstance by 1 degree

Therefore ifQ is the quantity of heat supplied to thesubstance of mass m and the temperature rise of it is

,then:

Q = mc , unit is Joules The quantity mc is termed the heat capacityC of the

substance which is the quantity of heat required to raise itstemperature by 1 K.

i.e. C = mc


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Examples of c for some substances

(1) Water = 4200 Jkg-1K-1

(2) Copper = 400 Jkg-1K-1


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Specific Latent Heat of Vaporisation, lv

The specific latent heat of vaporisation or evaporation of aliquid is the quantity of heat Q required to convert unitmass of it, at its boiling point, into vapor at the sametemperature.

The quantitys unit is Jkg-1.

Q = m x lv The latent heat of vaporisation is the heat absorbed to

cause a given liquid to undergo a liquid-to-vapour phasechange at its constant boiling temperature.


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Specific Latent Heat of Fusion, lf

The specific latent heat of fusion of a solid is the quantity ofheat required Q to convert unit mass of it, at its meltingpoint, into liquid at the same temperature.

The quantity has a unit of Jkg-1.

Q = m x lf The latent heat of fusion is the heat needed by a solid

when it undergoes a solid-to-liquid phase change (i.e.,melting) at its constant freezing (or melting) pointtemperature.


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Temperature Changes

Since = Q/(mc), a smaller mass substance will have agreater fall or gain in its temperature for the same amountof heat loss or gain by the substance at the sametemperature.

The advantage is reflected in the use of the thermometer toobtain the temperature of an object speedily since the heatcapacity at the thermometer junction is small.

For water, its higher specific heat capacity results in amuch slower rise in its temperature during heating.


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Example

An electric kettle with a 2.0 kW heating element has a heatcapacity of 400 Jkg-1. 1.0 kg of water at 20 C is placed inthe kettle. The kettle is switched on and it is found that 13minutes later the mass of water in it is 0.5 kg.

Ignoring heat losses, calculate a value for the specificlatent heat of vaporization of water. (Specific heat capacityof water = 4200 Jkg-1K-1).


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Solution

Total heat supplied = 2000 x 13 x 60 = 1.56 x 106 J

Heat used for kettle = C = 400 x (100 20) = 0.032 x 106 JHeat used to raise temperature of 1 kg of water from 20 to

100C = 1 x 4200 x (100 20) = 0.336 x 106 J

Heat used to change water at 100 C to steam at 100 C

= 1.56 x 106 - (0.032 x106 + 0.336 x 106)= 1.192 x 106 J

Mass of water changed to steam = 1.0 0.5 = 0.5 kg

lv = 1.192 x 106 /0.5 = 2.38 x 106 Jkg-1


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The law of conservation of energy and

thermodynamics Energy can neither be created nor destroyed

Thermodynamics is the study of processes involving the transfer

of heat and the doing of work

In thermodynamics it is necessary to define the system underconsideration

Examples of systems:

a) An ideal gas in a cylinder fitted with a piston

b) An electric heating coil in a container of liquid


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Transfer of energy

We have said that work is done when energy is transferred bymechanical means

We have also said that heat is a transfer of energy due to adifference in temperature

Work and heat both involve a transfer of energy, but by different

means We have also learnt that the internal energy of a system is the

total energy, ke and pe of the various parts of the system

For a system consisting of an ideal gas, the internal energy issimply the total ke of all the atoms and molecules of the gas

If heat were added to this system or work is done on it, it istransformed and appears as an increase to the internal energyof the gas as by the law of conservation of energy the energycannot just disappear

This addition of energy shows up as an increase in temperature


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First Law of Thermodynamics

The first law of thermodynamics states that the total energy in a

closed system is always constant which is basically a restatement

of the Principle of Conservation of Energy.

The increase in the internal energy of a system is equal to the

sum of the heat added to the system and the work done on it

The increase in internal energy is given the symbol U, heatadded is represented by Q and work done on the system by W

The change in internal energy (U =Uf- Ui) of a system is equalto the heat change (Q) to the system plus any associated workdone (W) to the system.

That is, U = Q + W Alternatively, U is equal to Q minus the work done W by the

system.

That is, U = Q - W


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Sign Convention:Q - is positive if heat is added to/absorbed by, the systemQ - is negative if given off by the systemW - is positive if work is done on the systemW - is negative if done by the system

U - is positive if an increase of internal energy i.e.overall gained by the system

U - is negative if overall lost by the system

The internal energy of a system is therefore dependent onthe state of the system at the point of time and is

independent of the process or path through which thesystem is brought from its initial to its final state.

The state of a system is defined by its pressure p , volumeV and absolute temperature T.


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Eg: Work Done by an Expanding Gas

Consider a gas of pressure p contained in a cylinder fitted with africtionless piston of cross-sectional area A. The force therefore Facting on the piston is pA. The cylinder and piston are insulatedso that no heat can enter or leave the gas

If work is done on the gas by pushing the piston in, W is positive

Hence U = 0 + W If the piston moves through a small distance l such that p

remains constant through out the expansion process, the workdone by the expanding gas W is given by:

W = Fl = pAl = pV

When a gas is warmed so that it expands to increase its volumeby V, the heat supplied Q goes towards increasing the internal

energy of the gas

U as well as doing an external work given by:U = Q + pV


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Eg: an electric kettle containing water

The heater element provides heat to the system, i.e Q

No mechanical work is done on or by the water i.e W = 0

U = Q + 0

Hence internal energy and temperature rises


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Change of state

When a substance changes from solid to liquid, intermolecularbonds are broken, thus increasing the potential energycomponent of the internal energy

During the melting process the temperature does not changeand therefore the kinetic energy of the molecules does not

change Most substances expand on melting, thus external work is done

i.e thermal energy is supplied to the system and this thermalenergy is the latent heat

External work done is much greater during vaporisation and

thus the latent heat of vaporisation is much greater than latentheat of fusion

e.g for water

c = 4.20 x 103 Jkg-1

Lf= 3.36 x 105 Jkg-1

Lv = 2.26 x 106

Jkg-1


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Example

200 J of heat is added to a system, which does 150 J of work.

Find the change in internal energy of the system.

Solution

U = Q + W= 200 - 150 = 50 J


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Recap


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What about solids ?

If we think of gases and liquids as having large numbers of

atoms, ions or molecules in rapid random motion, then the

microscopic model explains that:

for solids, due to their rigidity, the atoms are held in more lessfixed vibration positions by much stronger inter-atomic forces

Atoms in solids can still move but are restricted ito vibration about

their equilibrium positions

In the change of state from a solid to liquid to gas, work must be

done to break the rigid inter-atomic forces so that the atoms canmove freely i.e. energy must be applied to change the state


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Kinetic theory model

Melting

We think of molecules, ions or atoms as having definite

equilibrium positions, but vibrating about these positions with

kinetic energy When we heat a solid, the kinetic energy will depend on the

temperature

As we come to the melting point, the energy supplied does not

increase the kinetic energy i.e. temperature of the solid, but

instead is used to overcome the forces between the atoms This means that the potential energy is increased, which is the

latent heat of fusion


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Boiling

Boiling

As heating continues, the atoms can now move freely in the

liquid phase, but are still close enough to experience inter-

atomic forces When the temperature is increased to the boiling point, if atoms

are to escape, these atomic forces must be overcome i.e. the

energy input is the latent heat of vaporisation causing molecules

to move far apart

When boiling, all particles have the energy to escape


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Evaporation

Boiling only occurs at a particular temperature for a givenatmospheric pressure

The molecules in a liquid do not all move with the same speed

A molecule with a high enough energy may escape from theattractive forces of the molecules in the surface of the liquid

This process can take place at any temperature

However the higher the temperature the greater the loss ofmolecules

Evaporation increases with the rate of increase of temperature

of the surroundings

Loss of the fastest molecules means the average speed andkinetic energy of those remaining falls, causing a temperaturefall i.e. cooling effect

Evaporation only takes place on the surface


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Isothermal Change

An isothermal expansion or compression is one where agas expands or is compressed at a constant temperature.

So for a certain mass of a gas, the relations between thepressure and volume is that which obeys Boyles laws

where pV = constant. Therefore Q = W where U = 0.


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Example

An ideal gas expands isothermally, doing 250 J of work.

What is the change in internal energy ?

How much heat is absorbed in the process?


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Adiabatic Change

An adiabatic expansion or compression is one where no heatenters or leaves the gas.

In an adiabatic expansion, the external work is done wholly at theexpense of the internal energy of the gas, and the gas thereforecools.

In an adiabatic compression, all the work done on the gas resultsin a rise in the gass temperature.

Therefore U = -W where Q = 0.

f d f


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Refrigerators and the 2nd Law of

thermodynamics

The 2nd law of thermodynamics states that it is impossibleto produce an engine that will generate work by extractingheat without expelling some waste heat to a lowertemperature sink

A refrigerator is a heat pump which transfers internalenergy from objects placed in the refrigerator to thesurroundings.

The amount of heat transferred to the surroundings Q1 isequal to the heat from the interiorQ2 plus heat convertedfrom the electrical mains W.

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Section III 13 Thermal Properties of Materials