Chapter 15, Problem 31P

To determine

To find : The lowest temperature.

Answer to Problem 31P

  $-21.4°\text{C}$

Explanation of Solution

Given:

  $COP=5$

  $\begin{array}{c}{T}_H=29°\text{C}\\ =29+273\\ =302\text{K}\end{array}$

Formula used:

  $COP=\frac{T_L}{T_H-T_L}$

Calculation:

Substituting the values,

  $\Rightarrow 5=\frac{T_L}{302-T_L}$

  $\Rightarrow 6T_L=302\times 5$

  $\Rightarrow T_L=\frac{302\times 5}{6}$

  $\Rightarrow T_L=251.67\text{K}$

  $\Rightarrow T_L=-21.4°\text{C}$