d
(d) Initially \(\eta = \left( {1 - \frac{{{T_2}}}{{{T_1}}}} \right) = \frac{W}{Q} = \frac{1}{6}\) ...\((i)\)

Finally \(\eta ' = \left( {1 - \frac{{{T_2}'}}{{{T_1}}}} \right) = \left( {1 - \frac{{({T_2} - 62)}}{{{T_1}}}} \right) = 1 - \frac{{{T_2}}}{{{T_1}}} + \frac{{62}}{{{T_1}}}\)

\( = \eta + \frac{{62}}{{{T_1}}}\) ....\((ii)\)

It is given that \(\eta ' = 2\eta .\) Hence solving equation \( (i)\) and\((ii)\)

==> \({T_1} = 372\,K = 99^\circ C\) and \({T_2} = 310K = 37^\circ C\)