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

1. 41°C
2. 11°C
3. 21°C
4. 31°C

Correct answer: 31°C

Solution

The coefficient of performance (COP) of a refrigerator is given by COP = T_c / (T_h - T_c), where T_c and T_h are the absolute temperatures of the freezer and surroundings, respectively. Converting -20°C to Kelvin gives T_c = 253 K. Using COP = 5, we solve for T_h: 5 = 253 / (T_h - 253), leading to T_h = 304 K or 31°C.

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