First slide

Refrigerator

Question

A refrigerator works between $4^{0} C$ and $30^{0} C$ . It is required to remove 600 calories of heat every second in order to keep the temperature of the refrigerated space constant. The power required is (Take 1 cal = 4.2 Joules)

Moderate

A

$236.5 W$
B

$2365 W$
C

$2.365 W$
D

$23.65 W$

Solution

$Given, T_{2} = 4 ° C = 277 K, T_{1} = 30 ° C = 303 K$
$Q_{2} = 600 cal per second$
$Coefficient of performance, α = \frac{T_{2}}{T_{1} - T_{2}}$
$= \frac{277}{303 - 277} = \frac{277}{26} . Also, α = \frac{Q_{2}}{W}$
$∴ Work to be done per second = power required$
$= W = \frac{Q_{2}}{α} = \frac{26}{277} \times 600 cal per second$
$= \frac{26}{277} \times 600 \times 4.2 J per second = 236.5 W$

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