The coefficient of performance of a refrigerator is $5$ . If the temperature inside freezer is $-{20}^{\mathrm{o}}\mathrm{C}$, the temperature of the surrounding to which it rejects heat is:

• A

  ${\mathrm{41 }}^{\mathrm{o}}\mathrm{C}$
• B

  ${\mathrm{11 }}^{\mathrm{o}}\mathrm{C}$
• C

  ${\mathrm{21 }}^{\mathrm{o}}\mathrm{C}$
• Correct answer
  D

  ${\mathrm{31 }}^{\mathrm{o}}\mathrm{C}$

Solution

Coefficient of Performance = $\frac{{\mathrm{q}}_2}{\mathrm{w}}=\frac{{\mathrm{q}}_2}{{\mathrm{q}}_1-{\mathrm{q}}_2}=\frac{{\mathrm{T}}_{\mathrm{c}}}{{\mathrm{T}}_{\mathrm{H}}-{\mathrm{T}}_{\mathrm{C}}}=5$
 
${\mathrm{T}}_{\mathrm{C}}=5{\mathrm{T}}_{\mathrm{H}}-5{\mathrm{T}}_{\mathrm{c}}$

$6{\mathrm{T}}_{\mathrm{c}}=5{\mathrm{T}}_{\mathrm{H}}$

${\mathrm{T}}_{\mathrm{H}}=\frac{6}{5}\mathrm{ }\times 253 \mathrm{K}=303.6 \mathrm{K}=30.6 °\mathrm{C}=31 °\mathrm{C}$

Hence, the correct answer is option: 'D'.