Heat EnginesHeat Engines

A Brief Review of ThermodynamicsA Brief Review of Thermodynamics

ThermodynamicsThermodynamics

The science of thermodynamics deals with The science of thermodynamics deals with

the relationship between heat and work.the relationship between heat and work.

It is governed by two laws, neither of which It is governed by two laws, neither of which

have ever been proved.have ever been proved.

On the other hand no violations of either On the other hand no violations of either

law have ever been observed.law have ever been observed.

First Law of First Law of ThermodynamicsThermodynamics

The energy that can be extracted from a process The energy that can be extracted from a process can never be more than the energy put into the can never be more than the energy put into the processprocess

In other wordsIn other words Energy out = Energy inEnergy out = Energy in

This is essentially the law of conservation of This is essentially the law of conservation of energy, i.e.energy, i.e. Energy can be neither created nor destroyed, it can only Energy can be neither created nor destroyed, it can only

be converted from one form to anotherbe converted from one form to another

The second law of The second law of thermodynamicsthermodynamics

The first law is concerned with the totality of energy in a The first law is concerned with the totality of energy in a processprocess

The second law tells us how much work we can extract The second law tells us how much work we can extract from a given amount of heat.from a given amount of heat.

Carnot’s statement was to the effect that we cannot convert Carnot’s statement was to the effect that we cannot convert all the the available heat into work.all the the available heat into work.

The second law is also concerned with whether a process The second law is also concerned with whether a process can occur at all. For example,can occur at all. For example, Heat will always flow from a high to a low temperatureHeat will always flow from a high to a low temperature A gas under pressure will expand; compression does not A gas under pressure will expand; compression does not

occur naturallyoccur naturally

Heat EnginesHeat Engines

A heat engine is a device for extracting work from a hot A heat engine is a device for extracting work from a hot

fluid. For examplefluid. For example A car engine extracts power from the combustion of fuel with airA car engine extracts power from the combustion of fuel with air

A steam steam turbine extracts power from steamA steam steam turbine extracts power from steam

Both of these function by allowing a hot fluid to expand so Both of these function by allowing a hot fluid to expand so

as to cause motion in a critical component of the engine.as to cause motion in a critical component of the engine.

In the process, high grade energy is said to be degraded to In the process, high grade energy is said to be degraded to

lower grade energy.lower grade energy.

An ideal heat engineAn ideal heat engine

The diagram on the right The diagram on the right represents an ideal heat enginerepresents an ideal heat engine

Heat is added at constant Heat is added at constant temperature to the fluid at the temperature to the fluid at the high temperature sourcehigh temperature source

The fluid flows through an The fluid flows through an expansion device where work is expansion device where work is done, and the temperature of done, and the temperature of the fluid falls from Tthe fluid falls from THH to T to TLL

Heat is then rejected at constant Heat is then rejected at constant temperature at the low temperature at the low

temperature sourcetemperature source..

Closed Cycle Heat Closed Cycle Heat EngineEngine

The cycle in the previous The cycle in the previous slide is known as an slide is known as an open open cycle. cycle.

The closed cycle here has The closed cycle here has four stagesfour stages

Isothermal heat additionIsothermal heat addition Adiabatic expansionAdiabatic expansion Isothermal heat removalIsothermal heat removal Adiabatic compressionAdiabatic compression IsothermalIsothermal = const. Temp = const. Temp AdiabaticAdiabatic = perfectly = perfectly

insulated insulated

The Carnot EngineThe Carnot Engine

The cycles above are examples of the The cycles above are examples of the CarnotCarnot engine. engine. In the Carnot cycle all processes are reversible.In the Carnot cycle all processes are reversible. In a Carnot engine, the maximum work that can be done, and In a Carnot engine, the maximum work that can be done, and

hence the efficiency of the ideal engine depends on the hence the efficiency of the ideal engine depends on the temperatures Ttemperatures THH and T and TLL

The efficiency of a Carnot engine is given byThe efficiency of a Carnot engine is given by

H

L

H

LH

T

T

T

TT

1

The temperature is in the Kelvin or absolute scaleThe temperature is in the Kelvin or absolute scale This efficiency is called the Carnot efficiencyThis efficiency is called the Carnot efficiency

Practical heat engines Practical heat engines (1)(1)

The Carnot engine represents the theoretical limit The Carnot engine represents the theoretical limit and is not a practical engine.and is not a practical engine.

The main limitations of the Carnot engine are:The main limitations of the Carnot engine are: The processes in all four stages are reversible. For this The processes in all four stages are reversible. For this

to be the case they must all take place infinitely slowlyto be the case they must all take place infinitely slowly The work extracted on expansion is equal to the work The work extracted on expansion is equal to the work

required for compression, so no net work is extracted.required for compression, so no net work is extracted. A practical heat engine has a lower efficiency than A practical heat engine has a lower efficiency than

a Carnot engine, but can make more effective use a Carnot engine, but can make more effective use of the energy in the hot fluid.of the energy in the hot fluid.

Practical Heat Engines Practical Heat Engines (2)(2)

Practical Heat Engines include:Practical Heat Engines include: The Rankine cycle – basis of steam engines in power The Rankine cycle – basis of steam engines in power

stationsstations Otto and Diesel cycles – internal combustion enginesOtto and Diesel cycles – internal combustion engines Gas turbine Gas turbine

These have lower efficiencies than the Carnot These have lower efficiencies than the Carnot cycle but are permit useful work to be extracted.cycle but are permit useful work to be extracted.

The Rankine cycleThe Rankine cycle

This has two differences to the Carnot cycleThis has two differences to the Carnot cycle There must be reasonable temperature differences in There must be reasonable temperature differences in

the boiler and condenser to ensure that heat addition the boiler and condenser to ensure that heat addition and rejection occurs at an acceptable rateand rejection occurs at an acceptable rate

The turbine exhaust is completely condensed and The turbine exhaust is completely condensed and returned to the boiler by a pump. This uses very much returned to the boiler by a pump. This uses very much less energy than a compressor.less energy than a compressor.

These result in lower efficiencies than the Carnot These result in lower efficiencies than the Carnot cycle but permit useful work to be done.cycle but permit useful work to be done.

Other cyclesOther cycles

Otto, Diesel and Gas turbines all involve an initial Otto, Diesel and Gas turbines all involve an initial compression stage, but are otherwise open cycle compression stage, but are otherwise open cycle processes.processes.

Combined cycle gas turbine:Combined cycle gas turbine: This combines a gas turbine with a Rankine steam This combines a gas turbine with a Rankine steam

cycle to maximise the work extracted from the fuel. cycle to maximise the work extracted from the fuel. Efficiencies are much closer to Carnot efficiencies than Efficiencies are much closer to Carnot efficiencies than

in other practical cycle used to date.in other practical cycle used to date.

ExampleExample

Steam from a geothermal well is expanded in a Carnot Steam from a geothermal well is expanded in a Carnot engine from a temperature of 150engine from a temperature of 150C to 50C to 50C. How much C. How much work is extracted from 1kg of steam?work is extracted from 1kg of steam?

If the steam is heated to 250If the steam is heated to 250C before expansion, how C before expansion, how much work is now extracted in relation to the extra heat much work is now extracted in relation to the extra heat addedadded

Heat capacity of steam = 1.9 kJ kgHeat capacity of steam = 1.9 kJ kg-1-1 K K-1-1

00C = 273 KC = 273 K

SolutionSolution

Energy extracted = 1 Energy extracted = 1 1.9 1.9 100 = 190 kJ 100 = 190 kJ

EfficiencyEfficiency%24

273150

273501

After heating to 250:After heating to 250:

Energy extracted = 380 kJEnergy extracted = 380 kJ

Efficiency = 38%Efficiency = 38%

And Finally...And Finally...

Work is heat and heat is work Work is heat and heat is work

and all the heat in the universeand all the heat in the universe

is gonna coooool down!is gonna coooool down!

Yeh! That’s entropy man.Yeh! That’s entropy man.

Michael Flanders and Donald SwannMichael Flanders and Donald Swann