L07 Heat Engines

7/24/2019 L07 Heat Engines

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TA-in-charge:

Kalong Ng ( [email protected] )

L07 -- Heat Engines


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Todays Demo experiment

Explosion of fuel in confined space

Fire Syringe Stirling Engine Drinking Bird


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Heat, work and 2 nd law

We want to convert the heat energy to more desirable or

useful energy, such as kinetic energy and electricity. We know that heat flows from hot to cold

We want to Steal some heat energy from the heatdegradation process.

It can do something for us (do work)

But how much work can it do ?

Can all the internal thermal energy be cashed asusual work

What is the highest possible efficiency ?


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We know that

Heat energy is produced by burning fuel.

Hot object in a cool environment become less hot. The hotnessis measured by temperature.

The heat energy flow from region of high temperature to regionof low temperature is a spontaneous process.

This spontaneous process is an energy degradation processsince low temperature heat is less useful.

Heat energy at high temperature is of higher quality and is thusmore useful.

C O 2 CO 2 heat energy2H 2 O 2 2HO 2 heat energy

100 gram of C 2H16 heptanes:

C 7 H 16 11O 2 7CO 2 8H 2 O 1.15x10 6 cal heat


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We can indeed steal heat energy by using heat engine .

We can also reverse the heatflow by using heat pump .

Heat, work and 2 nd law

Fuel +

Oxygen

High temp

Heat energy

Low tempHeat energy

Heatengine

High qualityMechanical

Energy


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A low temperature differential Stirlingengine is a device used to obtainmechanical energy from the heat flow

between the atmosphere and a slightlyhotter or colder source.

A cup of hot coffee or human hand can be a hot source and a bowl of ice acold source.

Heat is transferred to or from the airthrough the engine wall.

Low Temperature DifferentialSterling Engine.

Demo : LTD Stirling engine


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Video 13: Steam Engine


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Heat engines work by extracting mechanicalenergy from a temperature difference

! Heat engines -- machines to do mechanical work that waspreviously done by animal and human muscles.

! Typically a machine is powered by a heat engine burning fossilfuel. The heat produced is transformed into mechanical work.

! The conversion of mechanical work into heat has long beenrecognized. Heat as a form of energy was finally established bythe recognition of the mechanical equivalent of heat (Joule 1847).

! The amount of mechanical work or energy produced from heat byan engine is governed by the Laws of Thermodynamics.


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Do work with heat

W output =

Qhot ! Qcool

Qcool

Cold

Hot

Qhot

W output = Qhot

HotQhot

Complete conversion ofheat to work:

Forbidden by 2 nd law

Mechanical energy can convert completely to heat (e.g. pendulum).

Heat can only convert partially to work. Need temperaturedifference. Some heat must go to a lower temperature heat sink

You cannot convert 100% of

random kinetic energy(thermal energy) intoorganized mechanicalenergy.


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It is desirable to have

Heat expelled to the cold reservoir

Qc = 0

All the heat taken from the hotreservoir is converted to work,

Qh = W

The efficiency, e = 100 %

This is the perfect engine that we want.But it is impossible because of therestriction demanded by the second lawof thermodynamics .


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From heat to work : you always lose something

Let E = increase of internal energy of heat sink ( T = T cool )

" E = Qhot - W ,

Qhot = heat transferred from T hot

W = (useful) mechanical work done

Temperature of the heat sink will rise

W = Qhot - " E is always less than Qhot . This means:

Only some of the heat can be made to work. There is always someloss of energy to the heat sink.

Your engine will not run for ever. T hot will drop. T cool will rise.

Eventually the heat source and heat sink will have the same temp,your engine stops; even though you still have a lot of internal

energy (no perpetual motion).


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Maximally efficient machines Let us consider the efficiency of the best

possible machine (no friction)

Efficiency! = (output work)/(input heat) = W /QH

but W = QH - QL , so thatW output =

Qhot ! Qcool

Qcool

Cold

Hot

Qhot

Note that ! < 1, even for an ideal reversible engine, ! for real

(irreversible) engines are smaller (friction losses).

! =W

Q H =

Q H ! Q LQ H

= 1 ! Q LQ H


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Maximum efficient of a thermal engine

Q H T H

!Q LT L

or Q LQ H

!T LT H

! =W

Q H =

Q H ! Q LQ H

= 1 !Q LQ H

" 1 ! T LT H

For high efficiency, the high temperature T H should be as highas possible

Recall Entropy , in any spontaneously happened natural evolution

process, entropy never decrease. According to the Second Law of Thermodynamics, the total entropy of

the engine and its surroundings must not decreases in the process. Theentropy expelled to the cold reservoir ( Q c/T c) must be at least as muchas the entropy absorbed from the hot reservoir ( Q h/T h). Thus

S =QT


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Limitations to the theoretical efficiency

T H cannot be too high, otherwise components could melt;

T L is usually in the normal range of atmospheric temperatures. Friction cannot be eliminated. Lubrication reduces friction in bearings, but

there is some viscous drag with the oils themselves.

The efficiency of a typical gasoline engine is about:

! ! 1 "T

L (room temperature)T

H (gassoline burning temperature)= 1! 300(

K )550(gassoline burning temperature)

= 45% (ideal case)

The First Law of Thermodynamics says e cannot be greater than 1 . Wecannot get more than we have put in. ! You cant win .

The Second Law of Thermodynamics says ! cannot be equal to 1 . Wecan only get less than we have put in. ! You cant even break even .


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Carnot engine

A heat engine operating in anideal, reversible Carnot cycle

between two reservoirs is themost efficient engine possible

This sets an upper limit on theefficiencies of all otherengines.

The Carnot cycle starts withan isothermal expansion,followed by an adiabaticexpansion and isothermalcompression, and finally anadiabatic compression bringsthe system back to the starting

point.


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Isothermal expansion

The gas is placed in contact withthe high temperature reservoir, T h

The gas absorbs heat | Qh|

The gas does work W AB in raisingthe piston.

A ! B


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Adiabatic expansion

The base of the cylinder is replaced

by a thermally nonconducting wall. No heat enters or leaves the system.

The temperature falls from T h to T c The gas does work W

BC

B ! C


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Isothermal compression

The gas is placed in contact withthe cold temperature reservoir at T c

The gas expels energy Qc Work W CD is done on the gas

C ! D


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1919

Adiabatic compression

The gas is again placed against athermally nonconducting wall, sono heat is exchanged with thesurroundings

The temperature of the gasincreases from T c to T h

The work done on the gas is W DA

D ! A


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Treating the human body (37 0 C) as a heat engine, what is its possible maximum efficiency if the room temperature is 20 0 C ?

The work done by the engine is

shown by the area enclosed bythe curve, W eng The net work is equal to

|Q h | - |Q c|

! E int = 0 for the entire cycle

The efficiency of the enginedepends on the temperatures of

the reservoirs

Carnot Engine, PV Diagram


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Why Carnot cycle between two reservoirs isthe most efficient engine?

The 2 nd Law tells us that the total entropy of the engine plus itssurroundings can increase but not decrease.

The entropy extracted from the hot reservoir is just Q h / T h.

The entropy expelled to the cold reservoir is Q c / T c.

So the 2 nd law tells us that Q c / T c # Q h / T h or Q c / Q h # T c / T h

Plugging this result into ! = W / Qh

= 1 Q

c / Q

h , we have

1- T c / T h


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Run a heat engine in reverse, wehave a heat pump.

Energy is extracted from the cold

reservoir, QC , and transferred to thehot reservoir, Qh

This is not a natural direction ofenergy transfer, energy input in the

form of work done on the engine,W, is needed to accomplish it.

Heat pump


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Heat Pump and Refrigerators

Coefficient of Performance ( COP ) is defined by:

COP = (Heat extracted from the cold bath )/(Work input )

For a reversible refrigerator

For a reversible heat pump

Note that as defined, COP can be greater than 1

COP cooling = benefit cos t

= Qcool W

= Qcool Qhot ! Qcool

= T cool T hot ! T cool

COP heating =benefit

cos t =

Qhot W

=Qhot

Qhot ! Qcool =

T hot T hot ! T cool


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hot Q

W input = Qhot ! Qcool

Qcool

Cold

Hot

Qhot


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In the warmer months, the heat pump acts like an air conditioner,removing heat from the air inside home and transferring it outside.During colder months, heat from outdoor air is extracted and transferredto the interior of your home.

Using electricity as

energy source, heatpumps are used foreither heating orcooling the room by

transferring heatbetween two reservoirs.

Heat pump


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Energy advantage of heat pump

A typical heat pump has a COP of 3 to 4.

Electric Heater: electric resistance heater using one kilowatt-hour of

electric energy can transfer only 1 kWh of energy to

heat your house at 100% efficiency.

Heat Pump: 1 kWh of energy used in an COP = 3 electric heat

pump could "pump" 3 kWh of energy from the cooleroutside environment into your house for heating.

Problem with heat pump: compressor is expensive, complex to maintain, and userefrigerants. Some hotels in HK are using heat pump to warm swimming pools


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Refrigerator: How does it work

Liquid (Freon) vaporizes in anevaporator in the cold region, absorbsheat there, colder region gets colder

An engine (compressor) draws the

vapor to the outside hotter region,compress it to a liquid. Liquid heats up,and gives heat to the hotter region(hotter region gets hotter) to cool down.

Engine pumps the liquid back to thecooler region, which vaporize again


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Example

For every joule of electrical energy consumed by an air conditioner,

20 joules of heat is dumped outside of the room. If the roomtemperature is 20 oC, what is the temperature outside (in oC) ?(assume that the air conditioner is operating at highest possibleefficiency)

hot input

hot cool

T Heat dumped to hot object W

T T = !

"

20 1(273 20)

308 K = 35 C

hot

hot

hot

T J J

T

T

= !

" +

=


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A refrigerator has an COP of 9. The room temperature is 27 oC.

What is the lowest possible temperature in the interior of therefrigerator ?

9(273 27)

270 3

cool cooling

hot cool

cool

cool

cool

T COP

T T

T T

T K C

=!

=

+ !

= = !

Example


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Environmental issue:refrigerator

Chloro-Flouro-Carbon or CFC is the gasused in old refrigerators (brand name:Freon)

Harmful to environment: deplete ozone

Ozone protects against UV

CFCs, when released, rise to the stratosphere. Once there, UV light decomposeCFC to release chlorine (Cl) , which react with ozone (O 3) molecules. Eventuallythe chlorine atom is removed from the atmosphere by other reactions.

The chlorine atoms are recycled in these reactions, and can attack other ozonemolecules. A single chlorine atom, released by the action of UV radiation onCFCs, can destroy catalytically tens of thousands of ozone molecules duringits residence in the stratosphere.

CFCs from refrigerators, air conditioners make an increasing hole in the ozonelayer above Antarctica.

l f f


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Replacement of CFCs as refrigerants

HCFC

HCFCs are compounds containing carbon, hydrogen,chlorine and fluorine. The HCFCs have shorteratmospheric lifetimes than CFCs and deliver less reactive

chlorine to the stratosphere

Less stratospheric ozone depletion than CFCs.

They still contain chlorine and have the potential to destroy

stratospheric ozone, they are temporary replacements forthe CFCs.

L07 Heat Engines

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