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2nd Law: Heat Engines
Heat Engines and Refrigerators
Chapter 19
Steam Engine: Type 1
• Heat engine – converts
some heat energy to
useful work
• Returns to its initial state
(closed cycle)
• Operating Temperatures
– TH and TL of the engine
• Cannot get all the work
out of the heat
Steam Engine: Type 2
• Most of our electric power comes from the
turbines
Car/Lawn Mower Engine
Efficiency of a Heat Engine
• Can’ convert all heat to work
e=W
QH
QH = W + QL
exhaust
heat
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e=W
QH
Heat Engine: Ex 1
An engine has introduces 2000 J of heat, and
discharges and loses 1500 J at exhaust.
Calculate the efficiency.
QH = W + QL
W = QH – QL
e = QH – QL = 1 - QL
QH
QH
e = 1 - QL
QH
e = 1 - 1500 J = 0.25 or 25%
2000 J
Heat Engine: Ex 2
An automobile engine has an efficiency of 20% and
outputs 23,000 J of work per second. Calculate
the heat input, QH, and the heat discharged, QL.
e=W
QH
QH = (23,000J/.20)
QH = 1.15 X 105 J
QH= W
e
Heat Engine: Ex 3
Calculate the maximum work that an engine
with 40% efficiency can perform if it absorbs
200 J of heat.
e = 1 - QL
QH
0.2 = 1 - QL
23,000J
-0.8 = - QL
23,000J
QL = 9.2 X 104 J
PV graphs
• Work = area under curve (one step)
• Work = inside curves (cycle)
e=W
QH
0.40 = W
200 J
W = 80 J
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Piston Example
• Work positive during expansion
• Work negative during compression
Example 1
Calculate the thermal efficiency of the following
Example 2
a. Calculate the moles of
gas at point 4 (pV=nRT)
b. Calculate the
temperature at points 1,
2, and 3
c. Calculate the net work
done in the following
process
d. Calculate the thermal
efficiency if Qh = 26.33 X
106 J
Example 3
Given the following
graph:
a. Calculate the
moles of gas in
the piston
b. Calculate the
Temperature at
point 2
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c. Calculate the work done from 1  2
d. Calculate the work done from 3  1 (W =
nRT ln(V1/V3)
e. Calculate the net work
f. Calculate the thermal efficiency if Qh = 200 J
Refrigerator
Carnot Efficiency
• Gas expands by
absorbing heat from
inside refrigerator
• Gives off heat to
back to cool
• Compressed by
compressor
• Carnot Efficiency – Efficiency of an ideal engine
• All processes in the engine are reversible
• In reality, engines use irreversible processes
eideal = 1 - TL
TH
(all temperatures must be in KELVIN)
Carnot Efficiency: Ex 1
bc
Adiabatic
expansion
A steam engine operates between the
temperatures of 500 oC and 270 oC. What is
the maximum possible efficiency?
eideal = 1 - 543 = 0.30 or 30%
773
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Carnot Efficiency: Ex 2
Carnot Efficiency: Ex 3
A steam engine boiler operates at 500 K and the
exhaust is at 300 K. Calculate the Carnot
efficiency.
An engine manufacturer claims that an engine has a
heat input of 9.0 kJ at 375 K, and ouptputs 4.0 kJ
of heat at 225. Is this possible?
ANS: 40%
First calculate the Carnot Efficiency:
eideal = 1 - TL
TH
eideal = 1 - 225 = 0.40
375
Now we can calculate the actual efficiency:
e = 1 - QL
QH
e = 1 - 4.0 kJ
9.0 kJ
=
0.56
Example 4
A Carnot engine is cooled by water at Tc = 10oC.
Calculate the temperature in the hot reservoir
if the engine has a 70% thermal efficiency.
e = 0.56
This engine is not possible
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