PHYSICS 231 Lecture 31: Engines and fridges

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PHYSICS 231Lecture 31 Engines and fridges

• Remco Zegers
• Question hours Thursday 1200-1300
  1715-1815
• Helproom

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Metabolism
?UQW
Work done (negative)
Heat transfer Negative body temperature lt room
temperature
Change in internal energy Must be increased
Food!
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Metabolic rate
?U Q W
Metabolic rate rate in which food and oxygen are
transformed into internal energy (to balance
losses due to heat loss and work done).
W/?t Bodys efficiency ?U/?t
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Bodys efficiency
?U/?toxygen use rate can be measured
?W/?t can be measured
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Types of processes
A Isovolumetric ?V0 B Adiabatic Q0 C
Isothermal ?T0 D Isobaric ?P0
PV/Tconstant
First law of thermo- Dynamics ?UQW
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Isovolumetric processes (line A)

• ?V0
• W0 (area under the curve is zero)
• ?UQ (Use ?UWQ, with W0)
• In case of ideal gas
• ?U3/2nR?T
• if P? then T? (PV/Tconstant)
• so ?Unegative Qnegative
• (Heat is extracted from the gas)
• if P? then T? (PV/Tconstant)
• so ?Upositive Qpositive
• (Heat is added to the gas)

p
v
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Adiabatic process (line B)
p

• Q0
• No heat is added/extracted from the
• system.
• ?UW (Use ?UWQ, with Q0)
• In case of ideal gas
• ?U3/2nR?T
• if T?
• ?Unegative Wnegative
• (The gas has done work)
• if T?
• ?Upositive Wpositive
• (Work is done on the gas)

v
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isothermal processes
p

• ?T0
• The temperature is not changed
• Q-W (Use ?UWQ, with ?U0)
• if V?
• Wpositive Qnegative
• (Work is done on the gas
• and energy extracted)
• if V?
• Wnegative Qpositive
• (Work is done by the gas
• and energy added)

v
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isobaric process
p

• ?P0
• Use ?UWQ
• In case of ideal gas
• W-P?V ?U3/2nR?T
• if V? then T? (PV/Tconstant)
• W positive (work done on gas)
• ?U negative
• Q negative (heat extracted)
• if V? then T? (PV/Tconstant)
• W negative (work done by gas)
• ?U positive
• Q positive (heat added)

v
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Cyclic processes
The system returns to its original state.
Therefore, the internal energy must be the same
after completion of the cycle (?U0)
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Cyclic Process, step by step 1
Process A-B. Negative work is done on the
gas (the gas is doing positive work).
?U3/2nR?T3/2(PBVB-PAVA)
1.5(1E5)(50E-03)-(5E5)(10E-03)0 The
internal energy has not changed ?UQW so
Q?U-W12000 J Heat that was added to the system
was used to do the work!
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Cyclic process, step by step 2
Process B-C
?U3/2nR?T3/2(PcVc-PbVb) 1.5(1E5)(10E-3)-
(1E5)(50E-3)-6000 J The internal energy has
decreased by 6000 J ?UQW so Q?U-W-6000-4000
J-10000 J 10000 J of energy has been transferred
out of the system.
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Cyclic process, step by step 3
Process C-A
W-Area under P-V diagram W0 J No work was done
on/by the gas.
?U3/2nR?T3/2(PcVc-PbVb) 1.5(5E5)(10E-3)-
(1E5)(10E-3)6000 J The internal energy has
increased by 6000 J ?UQW so Q?U-W6000-0
J6000 J 6000 J of energy has been transferred
into the system.
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Summary of the process
A-B
B-C
C-A
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What did we do?
The gas performed net work (8000 J) while heat
was supplied (8000 J) We have built an engine!
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More general engine
turns water to steam
heat reservoir Th
WQh-Qc efficiency W/Qh e1-Qh/Qc
Qh
work is done
the steam moves the piston
work
engine
W
Qc
The efficiency is determined by how much of the
heat you supply to the engine is turned into work
instead of being lost as waste.
the steam is condensed
cold reservoir Tc
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Reverse direction the fridge
heat is expelled to outside
heat reservoir Th
Qh
work is done
a piston compresses the coolant
work
engine
W
Qc
the fridge is cooled
cold reservoir Tc
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The 2nd law of thermodynamics
1st law ?UQW In a cyclic process (?U0) QW
we cannot do more work than the amount of energy
(heat) that we put inside
2nd law It is impossible to construct an engine
that, operating in a cycle produces no other
effect than the absorption of energy from a
reservoir and the performance of an equal amount
of work we cannot get 100 efficiency
What is the most efficient engine we can
make given a heat and a cold reservoir?
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Carnot engine
A?B isothermal expansion
W-, Q
Thot
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Carnot cycle
inverse Carnot cycle
Work done by engine Weng WengQhot-Qcold efficien
cy 1-Tcold/Thot
A heat engine or a fridge! By doing work we
can transport heat
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Next lecture
Entropy and examples