(II) A restaurant refrigerator has a coefficient of performance of 4.6. If the temperature in the kitchen outside the refrigerator is 32°C, what is the lowest temperature that could be obtained inside the refrigerator if it were ideal?

The ratio of the heat removed from the low-temperature area inside a refrigerator to the work done by the refrigerator to remove the heat is termed as the coefficient of performance of the refrigerator (COP).

The expression for the coefficient of performance is given as:

\({\rm{COP}} = \frac{{{Q_{\rm{L}}}}}{W}\)

The coefficient of performance is \(COP = 4.6\).

The temperature outside the refrigerator is \({T_2} = {\rm{32}}\circ {\rm{C}}\).

The expression for COP is given by:

\({\rm{COP}} = \frac{{{T_1}}}{{{T_2} - {T_1}}}\)

Substitute the values in the above expression.

\(\begin{array}{c}4.6 = \left( {\frac{{{T_1}}}{{\left( {{\rm{32}}\circ {\rm{C}} + 273} \right)\;{\rm{K}} - {T_1}}}} \right)\\{T_1} = 251\;{\rm{K}}\end{array}\)

Thus, the lowest temperature at ideal condition is \(251\;{\rm{K}}\).