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Mechanical Properties Of Fluids

Question
CBSEENPH11020647

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

  • 31o C

  • 41o C

  • 11o C

  • 21o C

Solution

A.

31o C

COfficient of performance (β) of a refrigerator is defined as the ratio of the quantity of heat removed per cycle to the work done on the substance per cycle to remove this heat.
Given, coefficient of performance of a refrigerator, β = 5
Temperature of surface i.e., inside freezer,
T2 = - 20o C = - 20 +273 = 253 K
The temperature of surrounding i.e heat rejected outside T1 =?
So, straight beta space equals space fraction numerator straight T subscript 2 over denominator straight T subscript 1 minus straight T subscript 2 end fraction

rightwards double arrow space 5 space equals space fraction numerator 253 over denominator straight T subscript 1 space minus space 253 end fraction

rightwards double arrow space 5 space straight T subscript 1 space equals space 1265 space equals space 253
rightwards double arrow space 5 space straight T subscript 1 space equals space 1518

straight T subscript 1 space equals space 1518 over 5 space equals space 303.6 space straight K
straight T subscript 1 space equals space 303.6 space minus 273 space equals space 31 to the power of straight o space straight C