Thermal Physics AHL Topic 10. Thermodynamics Thermodynamics is the study of heat and its...

Thermal Physics

Topic 10

Thermodynamics

Thermodynamics is the study of heat andits transformation into mechanical energy,

as heat and work.

The word is derived from the Greek meaning

‘movement of heat’.

It was developed in the mid 1800’sbefore atomic and molecular theory was developed.

Thermodynamics

Work is defined as:

The quantity of energy transferred from one system to another by ordinary mechanical processes.

Heat is defined as:

A transfer of energy from one body to another body at a lower temperature.

Thermodynamics

From this we can see that thermodynamics describes the relationship between heat and work.

To distinguish the two:Heat is the transfer of energy due to a temperature difference.

Work is the transfer of energy that is not due to a temperature difference.

ThermodynamicsThe foundation of this area of study isThe law of conservation of energy

and the fact that heat flows from hot to cold.

In discussing thermodynamics, we will refer to different systems.A system is just a group of objects we wish to consider.Everything else in the universe will be called the environment.

Thermodynamics

Consider a hot gas separated from a cold gas by a glass wall.

In macroscopic terms,we know that the hot gas gets cooler and the cool gas gets hotter.

The molecules in the hot gas hit the glassand set those molecules in faster motion.

Thermodynamics

This then sets in train a set of collisionswhich sees the energy being transferred to the cold gas.

If we were to observe a single collision,we could analyse the energy transfer

using the laws of mechanics.

Thermodynamics

We could say that one molecule has transferred energy

by doing work on another.

Heat is therefore the work done on a molecular level.

Thermodynamics

This is not the complete story.

Although the cool gas contains, on average,slower molecules than in the hot gas,

it does contain some fast moving molecules.

Likewise, the hot gas contains slow moving molecules.

Thermodynamics

From above, it should be possible to for the cold gas to transfer

energy to the hot gas

So the cool gas would get coolerand the hot gas hotter.

This does not disobey any classical theory of mechanics.

We do know however that this cannot occur.

Thermodynamics

To explain this, we cannot look at this the effects of single molecules

or even a few molecules.

We must, when discussing heat,look at the overall effects of a large number of moleculesand the average energiesand distribution of energies and velocities.

Thermodynamics

This is what is meant by a system of particles in thermodynamics.

A system could be any group of atoms,molecule or particles we wish to deal with.

It may be the steam in a steam engine,the earth’s atmosphere

or the body of a living creature.

Thermodynamics

The operation of changing the system from its initial state to a final state is called the,

Thermodynamic process.

Thermodynamics

During this process,heat may be transferred into or out of the system,

and work may be done on or by the system.

We assume all processes are carried out very slowly,

so that the system remains in thermal equilibrium at all stages.

Isothermal & Adiabatic Processes

Previously, we discussed the relationship between

pressure and volume and found that:

Isothermal & Adiabatic ProcessesWe also stated that this was true,

the temperature was constant.

A graph of P vs V is shown below.

The volume has increased from Vi to Vf

while the pressure has decreased.

The solid line is an isotherm,a curve giving the relationship

between V and P

at a constant temperature.

This is known as isothermic expansion.

The process of compression or expansion of a gas;

so that no heat enters or leaves the system,

is said to be adiabatic.

This comes from the Greek which means ‘impassable’.

Adiabatic changes of volume can be achieved by;

performing the process so rapidly that,heat has little time to enter or leave the system,like a bicycle pump.

Or by thermally insulating a system;from its surroundings,with Styrofoam.

A common example of a near adiabatic system;

is the compression and expansion of gases,

in the cylinders of a car engine.

Compression and expansion occur too rapidly;

for heat to leave the system.

When work is done on a gas by;adiabatically compressing it,the gas gains internal energy,and becomes warmer.

When the gas adiabatically expands;it does work on the surroundings,and gives up its internal energy,and becomes cooler.

Adiabatic processes occur in the atmosphere in large masses of air.

Due to their large size,mixing of different pressures

and temperatures

only occur at the edges of these large massesand do little to change

the composition of these air masses.

As it flows up the side of a mountain;its pressure reduces,

allowing it to expand and cool.

The reduced pressure resultsin a reduced temperature.

It has been shown that dry air will dropby 10oC

for every kilometre it rises.

Air can flow over high mountainsor rise in thunderstorms

or cyclones

many kilometres.

If a mass was 25oC at sea level and was lifted 6 kilometres,

its temperature would become -35oC.

An air mass that was -20OC at 6 km,would be 40oC at sea level.

An example of this is when cold air is blown over the Mt Lofty Ranges.Warm moist air is cooled as it rises over the ranges

starts to rain.

On the other side, the air begins to warm as it flows down the other side

causing a warm wind.

As the Mt Lofty ranges are not very high;the change in temperature is not as great,

compared to the Rocky Mountains in the USA..

P – V DiagramsThermodynamic processes can be represented by pressure - volume graphs.

P – V Diagrams

In the, an ideal gas is expanding isothermally,

absorbing heat Q,

and doing work W.

The system has not been restored;to its original state,

at the end of the process.

P – V Diagrams

The previous diagram is from a reversible heat engine.Process 1-2 takes place at a constant volume;

Isochoric

process 2-3 is adiabatic,process 3-1 is at a constant pressure;

Isobaric.

P – V Diagrams

In the next case;

the volume of an ideal gas is decreased,by adding weight to the piston.

The process is adiabatic (Q = 0).

P – V Diagrams

P – V DiagramsThe process is as shown below on a graph.

P – V Diagrams

In the next case,the temperature of an ideal gas is raised from T;

to T + T,by a constant pressure process.

Heat is added;and work is done,in lifting the loaded piston.

P – V Diagrams

P – V DiagramsThe process is shown below on a P-V diagram

P – V Diagrams

The work;PV,

is the shaded area under the line,

connecting the initial and final states.

Work Done By a Gas

To calculate the work done in a process,some Year 10 knowledge is important.

Imagine the pressure is kept constant during a process.

Work Done By a Gas

If the gas expands slowly against the piston;the work done to raise the piston is the force F multiplied by the distance d.

But the force is just the pressure P of the gas;

multiplied the area A of the piston,

F = PA.

Work Done By a Gas

W = Fd = PAd

W = PV = p(V2 – V1)

The sign of the work done depends on whether the gas expands or is compressed.

Work Done By a Gas

If the gas expands,V is +ive and

work is +ive.

The equation also is valid if the gas is compressed.

1st Law of Thermodynamics

A long, long time ago;heat was thought to be an invisible fluid,

called a caloric,

which flowed like water,

from hot objects,

to cold objects.

Caloric was conserved in its interactions which led to the discovery of the conservation of energy.

Within any system,the less heat energy it has,

the more ordered is the motion of its molecules.

This can be seen in solids;where the molecules all vibrate,

about a mean position.

As heat is added;the more disorderly the motion until in a gas,

we say that all molecules,

move in random motion.

In a sense then, heat is the disordered energy of molecules.

There can be no heat in a single molecule.

Heat is a statistical concept;applies only to a large number of molecules.

It is only when there is a great number of molecules

does the concept of random

or disorderly movement have meaning.

The discussion of heat,internal energy and temperature.

Has given rise to the law of conservation of energy,

and when applied to thermal systems,

is often referred to as the,

First law of thermodynamics.

In a general form it is:

Whenever heat is added to a system,it transforms to an equal amount of some other form of energy.

The added energy does one or both of two things to the system:

1. It increases the internal energy of the system if it remains in the system.

2. It does external work if it leaves the system.

Heat added = increase in internal energy + external work done by the system.It can also be described mathematically: Q = U + W

Q = heat energyU = internal energyW = work

For an isolated system;W = Q = 0 and U = 0

This can apply to a number of cases:

1.Adiabatic Processes.

In this case, no heat enters or leaves the system,

ie Q = 0.

Substituting this into the 1st Law;

0 = U + W or,U = -W.

This means that if work is done;there must be a decrease,

in the internal energy of the system.

2. Constant Volume Processes.

(Isovolumetric or Isochoric Process)

If the volume of a system is held constant;the system can do no work,

ie W =0.

Q = U.

If heat is added to the system;Q is +ive,

the internal energy of the system increases.

The converse is also true.

3.Cyclical Processes.

There are processes in which;after certain interchanges of heat and work,

the system is returned to its initial state.

No property of the system can change,including the internal energy,

ie U =0.

Q = W.

The net work done must exactly;equal the net amount of heat transferred.

4.Free Expansion.

This is an adiabatic process;no work is done on or by the system,

ie Q = W = 0.

An example of this is given below.

A gas confined in an insulated container;is released into another container,that originally was a vacuum and then waiting until an equilibrium is established.

as shown below.

No heat is transferred because;of the insulation

No work is done because;the expanding gas rushes into an evacuated space,

its motion unopposed by any counteracting pressure.

A summary is given:

Process Restriction Consequence

Adiabatic Q = 0 U = -W

Const V W = 0 U = Q

Closed Cycle U = 0 Q = W

Free Expansion Q = W = 0 U = 0

Thermodynamic Cycles

A thermodynamic cycle is;where heat may be transferred into (or out of),a system,or work may be done on or by the system.

It is assumed that all transfers are done;very slowly so,the system remains essentially,in thermodynamic equilibrium at all stages.

Thermodynamic CyclesAn engine is a device that changes heat into mechanical work.Examples include:The steam engine

external combustion

Petrol & dieselinternal combustion engines.

It is impossible to convert all the heat energy into mechanical work.

Consider the internal combustion engine.

Once the fuel is injected into the cylinder;the piston moves up,

compresses the gas,

Q = 0.

Spark plug fires,temperature increases.

Adiabatic expansion pushes the piston down,

burnt gases are pushed out.

A heat engine is a device that changes internal energy into mechanical work.

Examples include;Steam engine,

Internal combustion engine,

Jet engine.

The mechanical work can only be obtained when;

heat flows from a high to low temperature,

only some of the heat is transferred into work.

Every heat engine will:1. absorb internal energy from a reservoir of

higher temperature.2. convert some of this energy into

mechanical work expel the remaining energy to some lower temperature reservoir,

often called a sink.

Sadi Carnot;a French engineer,In 1924,

Analysed the compression and expansion of in a heat engineMade a fascinating discovery

when he examined the ideal engine,now called a Carnot engine.

The upper fraction of heat that can be converted to useful work;

even under ideal conditions,

depends on the temperature difference between,• the hot reservoir and the cold sink.

The cycle starts at a in the diagram below.

a b The gas expands isothermally by

adding heat QH at temp TH.

b c Gas then expands adiabatically

no heat is exchanged but temp drops to TL

c d Compressed at const temp TL and heat QL flows

d a Gas then compressed adiabatically to its original state.

His equation gives the ideal or Carnot efficiency of a heat engine.

The efficiency of the cycle only depends on;

the absolute temperature of the high and,

low temperature reservoirs.

The greater the difference between them;the greater the efficiency.

Entropy

Heat flows naturally from a hot object to a cold object; heat will not flow spontaneously from a cold object to a hot object.

Clausius introduced the word entropy;from the Greek words meaning,

transformation content.

2nd Law of Thermodynamics

Entropy is a function of;the state of the system.

Entropy can be interpreted as;a measure of of the order or disorder of a system.

A coin, when put flat on a table;cannot spontaneously rise into the air,

suddenly get too hot to touch,

flatten out to something twice its diameter.

These phenomena can easily be explained.

Each of these situations requires energy to be added to the system and so violate the conservation of energy.

We also know that coffee in a cup cannot;spontaneously cool down and start to swirl around,

one end of a spoon gets hot while the other end cools down.

molecules of air in the room do not move to one corner of the room and stay there.

These events however do obey the conservation of energy

and the first law of thermodynamics.

The coffee could get its energy from the cooling process,

the hot end of the spoon could get its energy from the cool end

molecules of air do not need to change their kinetic energy, only their position.

These events, however, do not happen although the reverse does happen.

There are many other cases where an event will happen in one direction but not the other.

The direction in which natural events happen is

Determined by the Second Law of Thermodynamics.

It can be described on a macroscopic and microscopic base:

No device is possible whose sole effect is to transform a given amount of heat completely into work.

This is the Kelvin-Planck formulation of the Second Law.

The second law suggests that everything;is tending to disorder.

Heat is a lower form of energy;so when heat is given off,it suggests that the system is tending to disorder.

When your parents ask you to clean your room, you might like to suggest that you are only obeying the second law of thermodynamics.

According to Clausius, the change in entropy S of a system;

when an amount of heat Q is added to it,

by a reversible process,

at constant temperature, is given by:

S = Q/T

The units of entropy are J K-1

In the example, although one part of the system decreased in entropy;

the total entropy for the system increased.

The second law stated in terms of entropy becomes:The entropy of an isolated system never decreases. It can only stay the same or increase.

Entropy can only remain the same;for an idealised (reversible) process.

For any real process;the change in entropy is greater than zero.

The general statement of the second law of thermodynamics becomes:

The total entropy of any system plus that of its environment increases as the result of any natural process.

Although the entropy of one part of the universe may decease in any process;

the entropy is some other part of the universe increases by a greater amount,

the total entropy always increases.

In the process of heat conduction from a hot body to a cold one;

entropy increases and order goes to disorder.

Useful work can be obtained while there is a temperature difference but;

when the two heat reservoirs reach the Vale temperature,

no work can be obtained from them.

No energy is lost, it instead becomes less useful;

the energy becomes degraded.

The natural outcome of this is that as time goes on;

the universe will reach a state of maximum disorder.

The whole universe will be at one temperature;

no work can be done.

All the energy will have become degraded;to thermal energy.

All change will cease.

This is known as heat death.

Refrigerators & Heat Pumps

Heat flows from the inside of warm houses in winter to the cold outside.

The reverse can happen,but only by imposing external effort

as do heat pumps.

Air conditioners or refrigerators use these.

The second form of the 2nd law of thermodynamics states:

It is not possible for heat to flow from one body to another body at a higher temperature, with no other change taking place.

A device that causes heat to move from a cold place to a hot place is called a refrigerator.

In the diagram on the left, heat Qc is

extracted from a low temperature reservoirthe food storage area

Some work W is done on the systemby an external agent.

The heat and work are combined and discharged as heat QH;

to a high temperature reservoir,• the kitchen.

The work shows up on the quarterly electricity bill;

done by the motor that drives the unit.

The diagram on the right shows a perfect refrigerator where no work is required.

This fridge is yet to be built.

In an air-conditioner,the low temperature reservoir is the room to be cooled

the high temperature reservoir is the outside air• where the condenser coils are located.

Again, the motor does the work.

For interestnot in syllabus

Both the fridge and the air-conditioner are rated by the amount of work they have to do.

The ratings are by the

coefficient of performance K.

This is defined from:

Design engineers want the performance of a fridge to be high as possible.

A value of 5 is typical for a household fridge,

while a room air-conditioner

range 2-3.

If there was a perfect fridge,the value of K = .

The 2nd Law & Technology

The second law indicates limits for technology.Heat engines and refrigerators cannot be perfect..It is not possible for heat to flow from one body to another;

at a higher temperature,with no other changes.

As the world is full of low-grade thermal energy from concept of entropy,

Why can’t we concentrate and harvest that energy?

Why not lower the temperature of the oceans by 1 oC

and use that enormous amount of energy?

It can be done but it requires;work be put into the system which requires,

energy to drive a fridge like machine.

This energy input would make it unfeasible from an energy perspective.

Every living creature from bacteriato higher life forms such as

Val Tudor

Extract energy from their surroundingsto increase their own organisation.

This tends to indicate that all life;Including Val,

plus their waste products

have a net increase in entropy.

The 1st law is a universal law for which no exceptions have been observed.

The 2nd law is a probability statement.

Given enough time,even the most improbable states could exist.

The 2nd law tells us the most probable event,not the only possible event.

The laws of thermodynamics are often put this way:

You can’t win,because you can’t get more energy out of a system than you put in,

You can’t break even,because you can’t even get as much energy as you put in,

You can’t get out of the game,entropy in the universe is always increasing.

TRY EXAMPLE 11.00 kg of water is to be converted to steam at standard atmospheric pressure. The volume changes from an initial value of 1.00 x 10-3 m3 as a liquid to 1.671 m3 as steam.

a) How much work is done by the system during this process?

b) How much heat must be added to the system during the process? (L = 2260 kJ kg-1)

c) What is the change in the internal energy of the system during the boiling process?

Solution – Part (a)

W = PVW = 1.01 x 105 (1.671 - 1 x 10-3)

W = 1.69 x 105 J

Solution – Part (b)

Q = mL

Q = 1 x 2260

Q = 2260 kJ

Q = 2.26 x 106 J

Solution – Part (c)

Q = U + WU = Q - WU = 2.26 x 106 - 1.69 x 105

U = 2.090 x 106 J

As the result is positive;the internal energy of the system,

has increased during the boiling process.

TRY EXAMPLE 2

A steam turbine uses steam at 127 oC which then is cooled to 27 oC. What is the ideal efficiency of the turbine?

Solution

Convert all temperatures to SI units

127 oC = 273 + 127 = 400 K

27 oC = 273 + 27 = 300 K

Efficiency = ¼

This means only 25% of the energy is converted into work while 75% is expelled as waste.

300-400 Efficiency

TRY EXAMPLE 3

A household fridge, whose coefficient of performance is 4.7, extracts heat from a cooling chamber at the rate of 250 J per cycle.

a) How much work per cycle is required to operate the fridge?

b) How much heat per cycle is discharged to the room, which forms the high temperature reservoir of the fridge?

Solution – Part (a)

From W = Qc /K

W = 250/4.7

W = 53 J

As work is done on the system, W = -53 J

Solution – Part (b)

The net work done per cycle must equal the heat transferred per cycle.

W = QH-Qc

QH= W + Qc

QH= 53 + 250 = 303 J

TRY EXAMPLE 4

An ice cube of mass 60 g is taken from a storage compartment at 0 oC and placed in a paper cup. After a few minutes, exactly half of the mass of the ice cube has melted, becoming water at 0 oC. Find the change in entropy.

Solution

Q = mL

Q = 0.06 x 3.34 x 105

Q = 1.002 x 104 J

S = Q/T

S = 1.002 x 104 /273

S = 36.7 J K-1

TRY EXAMPLE 5

A sample of 50.0 kg of water at 20.0 oC is mixed with 50.0 kg of water at 24 oC. Estimate the change in entropy.

Solution

The final temperature of the mixture will be 22 oC as we started with equal amounts of water. A quantity of heat,

Q = mcTQ = 50.0 x 4.18 x 103 x 2

Q = 4.18 x 105 J

Solution

flows out of the hot water and flows into the cold water.

The total change in entropy will be the sum of changes in entropy of the hot and cold water.

S = SH + SC

To calculate the entropy, we must use the average temperature of 23 oC for the hot water and 21oC for the cold water.

Solution

SH = 4.18 x 105/296

SH = -1.41 x 103 J K-1 (-ive as heat flows

out of the hot water)

SC = 4.18 x 105/294

SC = 1.42 x 103 J K-1

S = SH + SC

S = -1.41 x 103 + 1.42 x 103

S = 10 J K-1

Thermal Physics AHL Topic 10. Thermodynamics Thermodynamics is the study of heat and its...

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