Chapter 9, Problem 9.14P

Interpretation Introduction

Interpretation:

The minimum temperature of surrounding is to be calculated to maintain the house temperature at ${20}^{\circ }\text{C}$ during winter and the maximum temperature of surrounding is to be calculated to maintain the house temperature at ${25}^{\circ }\text{C}$ during summer.

Concept introduction:

A device used to heat buildings during winter and cool the during summer is a heat pump which is a reversed heat engine.

When used to heat the buildings in winter, is operates by absorbing heat from surroundings and rejecting it into the building.

The equation used to calculate the coefficient of performance is:

  $\left|\dot{W}\right|$ ...... (1)

Here,

  $\frac{\dot{W}}{\left|{\dot{Q}}_H\right|}=\frac{T_H-T_C}{T_H}$ ...... (2)

$T_H$ is the temperature of the house and $T_C$ is the surrounding temperature in winter.

When used to cool the buildings in summer, is operates by absorbing heat from building and rejecting it into the surroundings.

The equation used to calculate the coefficient of performance is:

  $\omega =\frac{\dot{W}}{\left|{\dot{Q}}_C\right|}$ ...... (3)

Here,

  $\frac{\dot{W}}{\left|{\dot{Q}}_C\right|}=\frac{T_H-T_C}{T_C}$ ...... (4)

$T_C$ is the temperature of the house and $T_H$ is the surrounding temperature in summer.