Heat Engines L05

Heat, work and 2nd law

•  Heat flows from hot to cold

•  It can do something for us (do work)

– But how much work can it do ?

– Can all the internal thermal energy be

“cashed” as usual work

•  What is the highest possible efficiency?

We know that •  Heat energy is produced by burning fuel.

•  Hot object in a cool environment become less hot. The hotness is measured by temperature.

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

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

•  Heat energy at high temperature is of higher quality and is thus more useful.

We want to •  “steal” all or some energy from the heat degradation process.

•  to reverse heat flow from region of low temperature to region of high temperature.

•  We can indeed steal heat energy by using heat engine.

•  We can also reverse the heat flow by using heat pump.

•  The Laws of Thermodynamics tell us how successful we are:

• the 1st Law: it is not possible to get more energy than the energy flowing through the engine

•  the 2nd Law: it is not possible to take all the heat energy flowing through the engine, but only some of it

Fuel + Oxygen

High temp Heat energy

Low temp Heat energy

Heat engine

High quality Mechanical

Energy

Low Temperature Differential Stirling Engine.

A low temperature differential Stirling engine is a device used to obtain mechanical energy from the heat flow between the atmosphere and a slightly hotter or colder source.

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

• Heat is transferred to or from the air through the engine wall.

Demo with liquid nitrogen (low temp demo) Liquid nitrogen (LN), a liquid with a low boiling point of –196 C, readily absorbs heat from objects in contact with it. This has some rather unexpected consequences.

•  Frozen banana serves as a hammer

•  Collapsed balloon when the gases inside freeze. The balloon recovers when taken out of LN as heat re-enter the balloon.

•  Floating nitrogen dashing on flat surface http://www.youtube.com/watch?v=gjsMV1MglA4

Fire syringe demo (high temp demo) •  Setting cotton wool on fire when the syringe plunger is pushed

down in syringe tube quickly .

Video 13: Steam Engine

Examples : steam engine, diesel engine, gasoline engine

Heat engines work by extracting mechanical energy from a temperature difference

Do work with heat

output

hot cool

WH H

=

−

coolH

Cold

Hot

hotH

output hotW H=

Hot

hotH

Complete conversion of heat to work:

Forbidden by 2nd law

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

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

You cannot convert 100% of “random” kinetic energy (thermal energy) into “organized” mechanical energy.

It is desirable to have

•  Heat expelled to the cold reservoir Qc = 0

• All the heat taken from the hot reservoir is converted to work,

Qh = W •  The efficiency, e = 100 % This is the perfect engine that we want. But it is impossible because of the restriction demanded by the second law of thermodynamics.

From heat to work: you always lose something Let ΔE = increase of internal energy of heat sink (T = Tcool)

•  ΔE = Hhot - W,

–  Hhot = heat transferred from Thot

–  W = (useful) mechanical work done

Temperature of the heat sink will rise •  W = Hhot - ΔE is always less than Hhot. This means:

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

•  Your “engine” will not run for ever.

–  Thot will drop. Tcool 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).

Maximally efficient machines •  Let us consider the efficiency of the best

possible machine (no friction) Efficiency ε = (output work)/(input heat) = W/HH

but W = HH - HL , so

output

hot cool

WH H

=

−

coolH

Cold

Hot

hotH

Note that ε < 1, even for an ideal reversible engine, ε for real (irreversible) engines are smaller (friction losses).

1H L L

H H H

H H HWH H H

ε−

= = = −

H hot

L cool

H HH H

=

=

Reversible engines are of maximum efficient

1 1

H L L L

H L H H

H L L L

H H H H

H H H TClausius showed thatT T H T

W H H H TH H H T

ε

= ⇒ =

−= = = − = −

1 L H L

H H

T T TT T

ε−

= − =

For high efficiency, your high temperature TH should be as high as possible

Limitations to the theoretical efficiency of any heat engine 

•  TH cannot be too high, otherwise components could melt;

•  TL 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.

Example 1 •  What is the maximum possible efficiency of an

engine using steam operating at a temperature of 100 oC on a day when the room temperature is 20 oC?

•  20 oC = 273+20=293 K and

•  100 oC = 273+100 = 373 K

•  Efficiency = (373 - 293) ÷ 373 = 0.21 (21 %)

Note: The temperature must be in Kelvin

Example 2 A small geothermal power station in Iceland pumps cold water into hot rock strata far below the Earth’s surface to be heated and returned at a constant temperature of 87 °C. The power station uses the hot water as the heat source for a heat engine which rejects energy to the much colder sea water near the station.

(a) When the temperature of the sea water is 7 °C, the power output from the heat engine is 5.0MW. Calculate:

(i) the maximum theoretical efficiency of the heat engine,

(ii) the rate at which heat energy must be transferred from the hot water if the engine works at the maximum theoretical efficiency,

(iii) the rate at which energy must be transferred to the sea water under these conditions.

(b) The power station produces electrical power with an overall efficiency which is much lower than the maximum theoretical efficiency of the heat engine. Give reasons for this lower efficiency.

(c) The overall efficiency of an oil-fired power plant of similar size to the geothermal station is over four times as great. Why the geothermal source was still preferred for the power station?

Answer (a) (i)                                                                            

Efficiency = (360 - 280) ÷ 360 = 0.222 (= 22.2 %) (ii) To get 5 MW, rate of energy exchange must be: Heat flow = 5.0 ÷ 0.222 = 22.5 MW (iii) Rate at which energy is passed to seawater = 22.5 MW - 5.0 MW = 17.5 MW   (b)

•  Friction within the heat engine. •  There will be heating in the generator windings as a current passes through the

wires. •  Losses to the atmosphere; •  Variations in sea temperature.

  (c)

Less pollution Oil is expensive and has to be transported to the site. Waste products might have to be treated.

Carnot engine •  A heat engine operating in an

ideal, reversible Carnot cycle between two reservoirs is the most efficient engine possible

•  This sets an upper limit on the efficiencies of all other engines.

•  The Carnot cycle starts with an isothermal expansion, followed by an adiabatic expansion and isothermal compression, and finally an adiabatic compression brings the system back to the starting point.

Isothermal expansion A → B • The gas is placed in contact

with the high temperature reservoir, Th

• The gas absorbs heat |Qh| • The gas does work WAB in

raising the piston.

Adiabatic expansion B → C • The base of the cylinder is

replaced by a thermally nonconducting wall.

• No heat enters or leaves the system.

• The temperature falls from Th to Tc

• The gas does work WBC

Isothermal compression C → D • The gas is placed in contact

with the cold temperature reservoir at Tc

• The gas expels energy Qc

• Work WCD is done on the gas

22 22

Adiabatic compression D → A

•  The gas is again placed a g a i n s t a t h e r m a l l y nonconducting wall, so no heat is exchanged with the surroundings

•  The temperature of the gas increases from Tc to Th

•  The work done on the gas is WDA

Treating the human body (370 C) as a heat engine, what is its possible maximum

efficiency if the room temperature is 200 C ?

Carnot cycle http://teaching.phys.ust.hk/phys1003/lecture_notes/Carnot cycle.swf

Otto Gasoline Engine The operation of a gasoline engine consists of an intake stroke, a compression stroke followed by the combustion of fuel initiated by a spark, next we have the power stroke in which work is done by the expanding gas, the final exhaust stroke expels the residue gas.

25

Heat pump

Run a heat engine in reverse, we have a heat pump. •  Energy is extracted from the cold

reservoir, QC, and transferred to the hot reservoir, Qh

•  This is not a natural direction of energy transfer, energy input in the form of work done on the engine, W, is needed to accomplish it.

Heat Pump -- Refrigerators

Coefficient of Performance (COP) of a reversible

refrigerator:

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

coscool cool cool

coolinghot cool hot cool

H H TbenefitCOPt W H H T T

= = = =− −

Note that as defined, COP can be greater than 1

hotQ

input hot coolW H H= −

coolH

Cold

Hot

hotH

Coefficient of Performance (COP)

•  For a reversible “refrigerator”

•  For a reversible “heat pump”

coscool cool cool

coolinghot cool hot cool

H H TbenefitCOPt W H H T T

= = = =− −

coshot hot hot

heatinghot cool hot cool

H H TbenefitCOPt W H H T T

= = = =− −

Heat pump

•  Heat added to hot object = heat removed form cold object + work done

•  Not against 2nd law: You are paying a price (do work) to move heat from cold to hot (against its natural direction)

coolinput

hot cool

THeat removed from cold object WT T

= ×−

input hot coolW H H= −

coolH

Cold

Hot

hotH

hotinput

hot cool

THeat dumped to hot object W

T T= ×

−

becomes less effective when the temp difference is big

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 transferred to the interior of your home.

Using electricity as energy source, heat pumps are used for either heating or cooling the room by transferring heat between two reservoirs.

Heat pump

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 cooler outside environment into your house for heating.

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

Can a room be cool down by opening the door of a refrigerator?

Opening a food refrigerator heats up the kitchen

Reason:

•  A refrigerator have to do work (by the compressor) to move

heat from inside to outside.

•  The heat you dump to outside is always more than what

take away from the inside.

•  The heat dumped to outside includes the compressor's

dissipated work as well as the heat removed from the inside

of the appliance.

Refrigerator: How does it work •  Liquid (Freon) vaporizes in an

“evaporator” in the cold region, absorbs heat 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 the cooler region, which vaporize again

Example 5

For every joule of electrical energy consumed by an air conditioner, 20 joules of heat is dumped outside of the room. If the room temperature is 20oC, what is the temperature outside (in oC) ? (assume that the air conditioner is operating at highest possible efficiency)

hotinput

hot cool

THeat dumped to hot object W

T T= ×

−

20 1(273 20)

308 K = 35 C

hot

hot

hot

TJ JT

T

= ×− +

=

A refrigerator has an COP of 9. The room temperature is 27oC. What is the lowest possible temperature in the interior of the refrigerator ?

9(273 27)270 3

coolcooling

hot cool

cool

cool

cool

TCOP

T TT

TT K C

=−

=+ −

= = −

Example 6

Environmental issue: refrigerator

•  Chloro-Flouro-Carbon or CFC is the gas used 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 decompose CFC to release chlorine (Cl), which react with ozone (O3) molecules. Eventually the chlorine atom is removed from the atmosphere by other reactions.

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

•  CFCs from refrigerators, air conditioners make an increasing “hole” in the ozone layer above Antarctica.

Environmental issue: refrigerator

Replacement of CFCs as refrigerants HCFC

•  HCFCs are compounds containing carbon, hydrogen, chlorine and fluorine. The HCFCs have shorter atmospheric 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 for the CFCs.