b
\(Given,\,{T_2} = {4^ \circ }C = 277\,K,{T_1} = {30^ \circ }C = 303\,K\)

\({Q_2} = 600\,cal\,per\,second\)

Coefficient of performance, \(\alpha  = \frac{{{T_2}}}{{{T_1} - {T_2}}}\)

\( = \frac{{277}}{{303 - 277}} = \frac{{277}}{{26}}\)

Also,\(\alpha  = \frac{{{Q_2}}}{W}\)

\(\therefore \) \(Work\,to\,be\,done\,per\,second=power\,required\)

\( = W = \frac{{{Q_2}}}{\alpha } = \frac{{26}}{{277}} \times 600\,cal\,per\,second\)

\( = \frac{{26}}{{277}} \times 600 \times 4.2\,J\,per\,second = 236.5\,W\)