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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

Question: (II) A 1.0-L volume of air initially at 3.5 atm of (gauge) pressure is allowed to expand isothermally until the pressure is 1.0 atm. It is then compressed at constant pressure to its initial volume, and lastly is brought back to its original pressure by heating at constant volume. Draw the process on a PV diagram, including numbers and labels for the axes.

An ideal gas undergoes an adiabatic expansion, a process in which no heat flows into or out of the gas. As a result,

(a) the temperature of the gas remains constant and the pressure decreases.

(b) both the temperature and pressure of the gas decrease.

(c) the temperature of the gas decreases and the pressure increases.

(d) both the temperature and volume of the gas increase.

(e) both the temperature and pressure of the gas increase

A particular car does work at the rate of about\({\bf{7}}{\bf{.0}}\;{\bf{kJ/s}}\)when traveling at a steady\({\bf{21}}{\bf{.8}}\;{\bf{m/s}}\)along a level road. This is the work done against friction. The car can travel 17 km on 1.0 L of gasoline at this speed (about 40 mi/gal). What is the minimum value for\({{\bf{T}}_{\bf{H}}}\)if\({{\bf{T}}_{\bf{L}}}\)is 25°C? The energy available from 1.0 L of gas is\({\bf{3}}{\bf{.2 \times 1}}{{\bf{0}}{\bf{7}}}\;{\bf{J}}\).

Question: (II) What is the temperature inside an ideal refrigerator-freezer that operates with a COP = 7.0 in a 22°C room?

Question:(II) A heat engine exhausts its heat at 340°C and has a Carnot efficiency of 36%. What exhaust temperature would enable it to achieve a Carnot efficiency of 42%?
See all solutions

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