Question

The coefficient of performance for a refrigerator can be :

• A. greater than $1$
• B. smaller than $1$
• C. equal to $1$
• D. None of these

Answer 1

The correct option is A greater than $1$

Refrigerator is a power absorbing device.

COP is nothing but the efficiency in different words.

$COP=\frac{Outpu}{Input}=$ (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, $COP=\frac{Q_2}{(Q_1-Q_2)}$,

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

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

as, $T_1>T_2$

so, $COP>1$ .

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