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Chapter 15: Q32P (page 412)

Question:(I) If an ideal refrigerator keeps its contents at 2.5°C when the house temperature is 22°C, what is its COP?

Short Answer

Expert verified

The coefficient of performance is \(14.1\).

Step by step solution

01

Given Data

The temperature of the contents in the refrigerator is\({T_1} = 2.5^\circ {\rm{C}}\).

The temperature of the house is \({T_2} = 22^\circ {\rm{C}}\).

02

Understanding ideal coefficient of performance

To calculate the ideal coefficient of performance of the refrigerator, divide the lower temperature (temperature of contents) with the difference in temperature from high to low.

03

Calculation of the COP of the ideal refrigerator

The relation for COP is

\({\rm{COP}} = \left( {\frac{{{T_1}}}{{{T_2} - {T_1}}}} \right)\).

Put the values in the above relation.

\(\begin{aligned}{l}{\rm{COP}} &= \left( {\frac{{\left( {2.5^\circ {\rm{C}} + 273} \right)\;{\rm{K}}}}{{\left( {\left( {22^\circ {\rm{C}} + 273} \right)\;{\rm{K}} - \left( {2.5^\circ {\rm{C}} + 273} \right)\;{\rm{K}}} \right)}}} \right)\\{\rm{COP}} &= 14.1\end{aligned}\)

Thus, \(14.1\) is the required COP.

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Most popular questions from this chapter

Can the temperature of a system remain constant even though heat flows into or out of it? If so, give examples.

Question: An ideal heat pump is used to maintain the inside temperature of a house at \({T_{{\rm{in}}}} = 22{\rm{^\circ C}}\) when the outside temperature is \({T_{{\rm{out}}}}\). Assume that when it is operating, the heat pump does work at a rate of 1500 W. Also assume that the house loses heat via conduction through its walls and other surfaces at a rate given by \(\left( {650\;{{\rm{W}} \mathord{\left/

{\vphantom {{\rm{W}} {{\rm{^\circ C}}}}} \right.} {{\rm{^\circ C}}}}} \right)\left( {{T_{{\rm{in}}}} - {T_{{\rm{out}}}}} \right)\). (a) For what outside temperature would the heat pump have to operate all the time in order to maintain the house at an inside temperature of 22°C? (b) If the outside temperature is 8°C, what percentage of the time does the heat pump have to operate in order to maintain the house at an inside temperature of 22°C?

(II) Calculate the probabilities, when you throw two dice, of obtaining (a) a 4, and (b) a 10.

The oceans contain a tremendous amount of thermal (internal) energy. Why, in general, is it not possible to put this energy to useful work?

A heat engine operates between a high temperature of about 600°C and a low temperature of about 300°C. What is the maximum theoretical efficiency for this engine?

(a) \( = 100\% \). (b) \( \approx 66\% \). (c) \( \approx 50\% \). (d) \( \approx 34\% \).

(e) Cannot be determined from the given information.
See all solutions

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