A) \[31{}^\circ C\]
B) \[41{}^\circ C\]
C) \[11{}^\circ C\]
D) \[21{}^\circ C\]
Correct Answer: A
Solution :
| Key Concept Coefficient of performance \[(\beta )\] of a refrigerator is defined, as the ratio of quantity of heat removed per cycle \[({{O}_{2}})\] to the work done on the working substance per cycle to remove this heat. |
| Given, coefficient of performance of a refrigerator, \[\beta =5\] |
| Temperature of surface i.e. inside freezer, |
| \[{{T}_{2}}=20{{\,}^{o}}C=-20+273=253\,K\] |
| Temperature of surrounding i.e. heat rejected outside \[{{T}_{1}}=?\] |
| So, \[\beta =\frac{{{T}_{2}}}{{{T}_{1}}-{{T}_{2}}}\Rightarrow 5=\frac{253}{{{T}_{1}}-253}\] |
| \[\Rightarrow \] \[5{{T}_{1}}-1266=253\] |
| \[\Rightarrow \] \[5{{T}_{1}}-1518\] |
| \[{{T}_{1}}=\frac{1518}{5}=303.6K\] |
| \[{{T}_{1}}=303.6-273=31{{\,}^{o}}C\] |
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