Question

An ideal refrigerator has a freezer at a temperature of $-{13}^{\circ }\text{C}$. The coefficient of performance of the engine used is $5$. The temperature of the air (to which heat is rejected) will be

• A. ${325}^{\circ }\text{C}$
• B. $325\text{K}$
• C. ${39}^{\circ }\text{C}$
• D. ${320}^{\circ }\text{C}$

Answer 1

The correct option is C ${39}^{\circ }\text{C}$

Refrigerator is ideal hence engine involved is Carnot's engine.
The temperature of freezer (sink), $T_2=-{13}^{\circ }\text{C}$
$\Rightarrow T_2=-13+273=260\text{K}$
Coefficient of performance, $\beta =5$
The coefficient of performance is defined as,
$\beta =\frac{T_2}{T_1-T_2}$
$\Rightarrow 5=\frac{260}{T_1-260}$
Or, $T_1-260=\frac{260}{5}$
Or, $T_1-260=52$
$\therefore T_1=312\text{K}$
$T_1=(312-273{)}^{\circ }\text{C}={39}^{\circ }\text{C}$