A) \[\frac{100}{3}J\]
B) \[100J\]
C) \[\frac{200}{3}J\]
D) \[150J\]
Correct Answer: D
Solution :
[d] The coefficient of performance of a refrigerator is given by \[\alpha =\frac{{{Q}_{2}}}{W}=\frac{{{Q}_{2}}}{{{Q}_{1}}-{{Q}_{2}}}\] Substituting the given values, we get \[\frac{1}{3}=\frac{{{Q}_{2}}}{200-{{Q}_{2}}}\] \[\Rightarrow 200-{{Q}_{2}}=3{{Q}_{2}}\Rightarrow 4{{Q}_{2}}=200\] \[\text{or }{{Q}_{2}}=\frac{200}{4}J=50J\] \[\therefore W={{Q}_{1}}-{{Q}_{2}}=200J-50J=150J\]
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