Question

The coefficient of performance of a refrigerator is $5$. If the temperature inside the freezer is $-20°C$ the temperature of the surroundings to which it rejects heat is?

Answer 1

Step 1: Given

Coefficient of performance, $\alpha =5$

Temperature of the freezer, $$\begin{gathered} T_2=-20°C \\ =253K \end{gathered}$$

Temperature of the surrounding$=T_1$

Step 2: Formula used

The coefficient of performance is given by $\alpha =\frac{T_2}{T_1-T_2}$, where $T_1$ is the temperature of the surrounding and $T_2$ is the temperature of the freezer.

Step 3: Determine the value of $T_1$

The coefficient of performance is given by,

$$\begin{gathered} \alpha =\frac{T_2}{T_1-T_2} \\ 5=\frac{253}{T_1-253} \\ {T}_1=303.6K \\ =30.6°C \end{gathered}$$

Therefore, the temperature of the surroundings is $30.6°C$