3.1 The Second Law of Thermodynamics and the Carnot Heat Engine 113
Th 273 .15 K+(40◦F− 32 ◦F)(
5K
9 ◦F)
294 .26 Kηhp
1
1 −
Tc
Th
1
1 −
277 .59 K
294 .26 K 17. 6Exercise 3.3
a.Calculate the coefficient of performance of a reversible refrigerator operating between an
interior temperature of 4.0◦C and an exterior temperature of 22.0◦C.
b.Assume that a house is heated by a heat pump that has a coefficient of performance equal to
50.0% of that of a reversible heat pump. If the interior temperature is 22. 0 ◦C and the exterior
temperature is 4. 0 ◦C, find the cost per joule of heating the house if electrical energy costs
$0.13 per kilowatt-hour.
c.If a real heat pump has an efficiency that is 50.0% of that of the reversible heat pump of part
a, find the cost per joule of heating a house in the United States if electrical energy costs
$0.13 per kilowatt-hour and if the temperatures are as in part b.PROBLEMS
Section 3.1: The Second Law of Thermodynamics and the
Carnot Heat Engine
3.1 a.A Carnot engine contains 0.250 mol of a monatomic
ideal gas as its working fluid. AssumeCVto be constant
and equal to 3nR/2. IfTh473 K,Tc373 K,
V 1 0 .600 L, and if the compression ratio (the ratio
V 3 /V 1 ) equals 6.00, find the efficiency and the values of
V 2 andV 4.
b.Calculatewfor each of the steps in the cycle of part a.
3.2A Carnot engine contains as working fluid 0.150 mol of
neon (assume ideal) withCV, m 3 R/2. IfTh600 K and
Tc373 K, find the values ofV 1 ,V 2 ,V 3 ,P 3 ,P 4 , andV 4 if
P 1 20 .00 atm andP 2 5 .00 atm.
3.3 Carbon monoxide is used as the fuel for a Carnot engine
with a high temperature of 450◦C and a cool temperature
of 100◦C. Determine how high the combustion of
1.000 mol of CO could lift a 1.00 kg mass near the
surface of the earth. Assume that all of the heat from the
combustion is transferred to the engine and assume
that the combustion takes place at 450◦C.
3.4A Carnot engine is operated by burning 1.00 mol of
methane at a temperature of 1000 K. The cool reservoir is
at 373 K.
a.Find the enthalpy change of the combustion reaction at
1000 K.b.Find the amount of work that can be done by the engine
when it burns this much fuel. Assume that no heat is
lost.
3.5 a.A steam engine operates with its boiler at 200◦C and a
pressure of 15.34 atm, and with its exhaust at a
temperature of 100◦C and a pressure of 1.000 atm. Find
the Carnot efficiency for these temperatures. What can
you say about the efficiency of the steam engine?
b. The boiler is reinforced to operate at 360◦C and a pres-
sure of 184 atm. If the exhaust remains at 100◦C, find
the percentage improvement in the Carnot efficiency.
c.If the coal that the steam engine in part b burns is
assumed to be pure graphite (not a good assumption)
find the mass of coal required to produce 10.00
horsepower for 1.000 hour, assuming the Carnot
efficiency. 1 horsepower746 watt746Js−^1.
3.6Assume gasoline to be puren-octane and assume that its
enthalpy change of combustion is approximately
independent of temperature. Calculate the height to which
combustion of 1.000 kg of gasoline can lift an automobile
with a mass of 1500 kg. Assume that the automobile engine
has a combustion temperature of 2000◦F and an exhaust
temperature of 1100◦F and that the engine has an efficient
75% as large as that of a Carnot engine operating between
these temperatures.