c
The efficiency \(\left( \eta  \right)\) of a Carnot engine and the coefficient of performance \(\left( \beta  \right)\) of a refrigerator are related as

\(\beta  = \frac{{1 - \eta }}{\eta }\)       \(Here,\,\eta  = \frac{1}{{10}}\)         \(\therefore \beta \frac{{1 - \frac{1}{{10}}}}{{\left( {\frac{1}{{10}}} \right)}} = 9.\)

Also, Coefficient of performance \(\left( \beta  \right)\) is given by \(\beta  = \frac{{{Q_2}}}{W}\)

where \(Q_2\) is the energy absorbed from the reservoir.

or,   \(9 = \frac{{{Q_2}}}{{10}}\)                          \(\therefore {Q_2} = 90\,J\)