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Problem Set 3
Due: See Website for due dates
Chapter 21: Entropy and the Second Law of Thermodynamics
Problems: 20, 25, 35, 37, 43
Question A
A pot is half-filled with water, and a lid is placed on the pot, forming a tight seal so that no
water vapor can escape. The pot is heated on a stove, forming water vapor inside the pot.
The heat is then turned off and the water vapor condenses back to liquid. Is this cycle
reversible or irreversible? Why?
Question B
Real heat engines, like the gasoline engine in a car, always have some friction between
their moving parts, although lubricants keep the friction to a minimum. Would a heat engine
with completely frictionless parts be 100% efficient? Why or why not? Does the answer
depend on whether or not the engine runs on the Carnot cycle? Again, why or why not.
Question C
(i) Is it a violation of the second law of thermodynamics to convert mechanical energy
completely into heat? (ii) To convert heat completely into work? Explain your answers.
Question D
(i) What would be the efficiency of a Carnot engine operating with TH = TC? Interpret your
answer. (ii) What would be the efficiency if TC = 0K and TH were any temperature above?
Interpret your answer.
Question E
Suppose you try to cool the kitchen of your house by leaving the refrigerator door open.
What happens? Why? Would the result be the same if you left open a picnic cooler full of
ice? Explain the reason for any differences.
Problem 20.20
Expand 1.00 mol of an monatomic gas initially at 5.00 kPa and 600 K from initial volume Vi
= 1.00 m3 to final volume Vf = 2.00 m3. At any instant during the expansion, the pressure p
and volume V of the gas are related by p = 5.00 exp[(Vi − V)/a], with p in kilopascals, Vi and
V in cubic meters, and a = 1.00 m3.What are the final (a) pressure and (b) temperature of
the gas? (c) How much work is done by the gas during the expansion? (d) What is ∆S for
the expansion? (Hint: Use two simple reversible processes to find ∆S.)
Problem 20.25
A Carnot engine has an efficiency of 22.0%. It operates between constant-temperature
reservoirs differing in temperature by 75.0 C°. What is the temperature of the (a) lowertemperature and (b) higher-temperature reservoir?
Problem 20.35
The cycle in the figure represents the operation of a gasoline internal
combustion engine. Volume V3 = 4.00V1. Assume the gasoline–air intake
mixture is an ideal gas with γ = 1.30.What are the ratios (a) T2/T1, (b) T3/T1,
(c) T4/T1, (d) p3/p1, and (e) p4/p1? (f) What is the engine efficiency?
Problem 20.37
A heat pump is used to heat a building. The outside temperature is 25.0°C, and the
temperature inside the building is to be maintained at 22°C.The pump’s coefficient of
performance is 3.8, and the heat pump delivers 7.54 MJ as heat to the building each hour. If
the heat pump is a Carnot engine working in reverse, at what rate must work be done to run
Problem 20.43
The figure represents a Carnot engine that works between
temperatures T1 = 400K and T2 = 150K and drives a Carnot
refrigerator that works between temperatures T3 = 325K and T4 =
225K. What is the ratio Q3 /Q1?