First slide

Refrigerator

Question

The temperature inside a refrigerator is ${t_{2}}^{0} C$ and the room temperature is ${t_{1}}^{0} C$ . The amount of heat delivered to the room for each joule of electrical energy consumed ideally will be

Moderate

A

$\frac{t_{2} + 273}{t_{1} - t_{2}}$
B

$\frac{t_{1} - t_{2}}{t_{1} + 273}$
C

$\frac{t_{1}}{t_{1} - t_{2}}$
D

$\frac{t_{1} + 273}{t_{1} - t_{2}}$

Solution

Heat delivered = $Q_{1}$
${COP}_{(β)} = \frac{t_{2} + 273}{t_{1} - t_{2}} = \frac{Q_{2}}{W} = \frac{Q_{1} - W}{W} = \frac{Q_{1}}{W} - 1$
$\frac{Q_{1}}{W} = 1 + \frac{t_{2} + 273}{t_{1} - t_{2}} = \frac{t_{1} + 273}{t_{1} - t_{2}}$

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