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

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

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

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

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

Solution

Temperature inside refrigerator ${t_{2}}^{0} C$ Room temperature ${t_{1}}^{0} C$
For refrigerator,
$\frac{Heat given to high temperature (Q_{1})}{Heat taken from lower temperature (Q_{2})} = \frac{T_{1}}{T_{2}}$
$\frac{Q_{1}}{Q_{2}} = \frac{t_{1} + 273}{t_{2} + 273}$
$\Rightarrow \frac{Q_{1}}{Q_{1} - W} = \frac{t_{1} + 273}{t_{2} + 273} or, 1 - \frac{W}{Q_{1}} = \frac{t_{2} + 273}{t_{1} + 273}$
$or \frac{W}{Q_{1}} = \frac{t_{1} - t_{2}}{t_{1} + 273}$
$T h e a m o u n t o f h e a t d e l i v e r e d t o t h e r o o m f o r e a c h j o u l e o f e l e c t r i c a l e n e r g y (W = 1 J)$
$Q_{1} = \frac{t_{1} + 273}{t_{1} - t_{2}}$

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