A Carnot engine having an efficiency of $\frac{1}{10}$ as heat engine, is used as a refrigerator.  If the work done on the system is 10J, the amount of energy absorbed from the reservoir at lower temperature is

In case of engine,

Engine efficiency = $\frac{work}{heatabsorbed}=\frac{W}{q_1}$

$\therefore \frac{W}{q_1}=\frac{1}{10}\Rightarrow \frac{10J}{q_1}=\frac{1}{10}$ or $q_1=100J$

When this engine is reversed, it takes in work W and heat $q_2$ from cold reservoir and ejects 100 J of heat to hot reservoir.

$\therefore$W + $q_2$= $q_1$

$\Rightarrow$ 10 + $q_2$= 100   or  $q_2$= 90J