heat engine
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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.
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