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Question

The coefficient of performance for a refrigerator can be :


A
greater than 1
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B
smaller than 1
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C
equal to 1
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D
None of these
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Solution

The correct option is A greater than $$1$$
Refrigerator is a power absorbing device.

COP is nothing but the efficiency in different words.

$$COP =\dfrac{Outpu}{Input} =$$ (Desired effect/ Work Input)

for a refrigerator working between two temperature limits, T1(higher) and T2(lower)

Refrigerator will be throwing the heat taking from the T2( Storage Space) to T1(Room or any exhaust at higher temperature).

COP= (Heat taken from the Storage Space)/(Work Input) = Q2/W, , where W in work input.

as, $$Q_1=Q_2+W$$

so, $$COP= \dfrac{Q_2}{(Q_1-Q_2)}$$,

applying the reversible refrigerator theory, Q can be replaced by temperature (100% Second Law Efficiency).

$$COP=\dfrac{T_2}{(T_1-T_2)}$$,

as, $$T_1>T_2$$

so, $$COP > 1$$ .

Generally T1 and T2 difference is less than T2 so efficiency is always greater than 1.

Physics

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