A) 5
B) 8
C) 6
D) 10
Correct Answer: A
Solution :
Coefficient of performance of the refrigerator is \[\beta =\frac{{{Q}_{2}}}{W}=\frac{{{Q}_{2}}}{{{Q}_{1}}-{{Q}_{2}}}=\frac{{{Q}_{2}}/{{Q}_{1}}}{1-{{Q}_{2}}/{{Q}_{1}}}\] \[=\frac{{{T}_{2}}/{{T}_{1}}}{1-{{T}_{1}}/{{T}_{2}}}=\frac{{{T}_{2}}}{{{T}_{1}}-{{T}_{2}}}\] where,\[{{T}_{1}}\]is temperature of source,\[{{T}_{2}}\]of sink. Given, \[{{T}_{2}}=273+27=300\text{ }K\] \[{{T}_{2}}=273+(-23)=250K\] \[\therefore \] \[\beta =\frac{250}{300-250}=\frac{250}{50}=5\] Coefficient of performance of refrigerator increases when\[{{T}_{1}}\]is small.
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