Chapter 21: Q. 33 (page 596)

The coefficient of performance of a refrigerator is $5.0$ . The compressor uses $10 J$ of energy per cycle.
a. How much heat energy is exhausted per cycle
b. If the hot-reservoir temperature is $27 ° C$ , what is the lowest possible temperature in ${}^{\circ}C$ of the cold reservoir?

Short Answer

Expert verified

a.Heat energy is exhausted per cycle is $60 J$ .

b.Lowest possible temperature $T_{c}$ is $- 23 ° C$ .

Step by step solution

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

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

$Q_{c} = Q_{h} + W$

$K = \frac{Q_{c}}{W} \Rightarrow Q_{c} = KW$

Substituting this we get,

$Q_{c} = Q_{h} - W = W (K + 1)$

$Q_{h} = 10 \cdot (5 + 1) = 60 J$

Calculation for lowest possible temperature (part 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,

$K = \frac{T_{c}}{T_{h} - T_{c}} = \frac{T_{h}}{T_{h} - T_{c}} - 1$

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

$T_{h} = (K + 1) (T_{h} - T_{c}) \Rightarrow - T_{h} K = - (K + 1) T_{c}$

T_{c} = T_{h} \frac{K}{K + 1}

The minimum temperature ,

$T_{c} = \frac{5}{5 + 1} \cdot (273 + 27) = 250 K$

In degrees centigrade,

$T_{c} = - 23 ° C$

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The coefficient of performance of a refrigerator is $5.0$ . The compressor uses $10 J$ of energy per cycle.
a. How much heat energy is exhausted per cycle
b. If the hot-reservoir temperature is $27 ° C$ , what is the lowest possible temperature in ${}^{\circ}C$ of the cold reservoir?

Short Answer

Step by step solution

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

Calculation for lowest possible temperature (part b)

One App. One Place for Learning.

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The coefficient of performance of a refrigerator is5.0. The compressor uses10Jof energy per cycle.a. How much heat energy is exhausted per cycleb. If the hot-reservoir temperature is27°C, what is the lowest possible temperature inC∘of the cold reservoir?

Short Answer

Step by step solution

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

Calculation for lowest possible temperature (part b)

One App. One Place for Learning.

Most popular questions from this chapter

Recommended explanations on Physics Textbooks

Translational Dynamics

Geometrical and Physical Optics

Physics of Motion

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Circular Motion and Gravitation

Oscillations

Study anywhere. Anytime. Across all devices.

The coefficient of performance of a refrigerator is $5.0$ . The compressor uses $10 J$ of energy per cycle.
a. How much heat energy is exhausted per cycle
b. If the hot-reservoir temperature is $27 ° C$ , what is the lowest possible temperature in ${}^{\circ}C$ of the cold reservoir?