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Chapter 21: Q. 33 (page 596)

The coefficient of performance of a refrigerator is5.0. The compressor uses10Jof energy per cycle.

a. How much heat energy is exhausted per cycle

b. If the hot-reservoir temperature is27°C, what is the lowest possible temperature inC∘of the cold reservoir?

Short Answer

Expert verified

a.Heat energy is exhausted per cycle is60J.

b.Lowest possible temperatureTcis-23°C.

Step by step solution

01

Calculation for heat energy is exhausted per cycle  (part a)

a.

As a result of the first law that was applied to refrigerators, we now have

Qc=Qh+W

K=QcW⇒Qc=KW

Substituting this we get,

Qc=Qh-W=W(K+1)

Qh=10·(5+1)=60J

02

Calculation for lowest possible temperature (part b)

b.

When the coefficient of performance is that of a Carnot refrigerator, the lowest value of the temperature of the cold reservoir is reached.

That is,

K=TcTh-Tc=ThTh-Tc-1

The value of the lower temperature can be separated as follows:

Th=(K+1)Th-Tc⇒-ThK=-(K+1)Tc

Tc=ThKK+1

The minimum temperature ,

Tc=55+1·(273+27)=250K

In degrees centigrade,

Tc=-23°C

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Most popular questions from this chapter

At what pressure ratio does a Brayton cycle using a monatomic gas have an efficiency of50% ?

FIGURE CP21.70shows two insulated compartments separated by a thin wall. The left side contains 0.060molof helium at an initial temperature of 600Kand the right side contains 0.030molof helium at an initial temperature of 300K. The compartment on the right is attached to a vertical cylinder, above which the air pressure is 1.0atm. A 10-cm-diameter,2.0kg piston can slide without friction up and down the cylinder. Neither the cylinder diameter nor the volumes of the compartments are known.

a. What is the final temperature?

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c. How high is the piston lifted due to this heat transfer?

d. What fraction of the heat is converted into work?

A car’s internal combustion engine can be modeled as a heat engine operating between a combustion temperature of 1500oC and an air temperature of 20oC with 30% of the Carnot efficiency. The heat of combustion of gasoline is 47kJ/g. What mass of gasoline is burned to accelerate a 1500kgcar from rest to a speed of 30 m/s?

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Rank in order, from largest to smallest, the thermal efficiencies η1to η4of the four heat engines in FIGURE Q21.5. Explain.
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