In the Carnot engine, when heat is taken from the source, the temperature of the source

The efficiency of a Carnot engine is $0.6$. It rejects a total of $20 \ J$ of heat. The work done by the engine is .... $J$.

State Carnot's theorem.

$A$ Carnot engine of efficiency $40 \%$ takes heat from a source maintained at a temperature of $500 \ K$. It is desired to have an engine of efficiency $60 \%$. Then,the source temperature for the same sink temperature must be (in $K$)

The work done by a Carnot engine operating between $300 \,K$ and $400 \,K$ is $400 \,J$. The energy exhausted by the engine is (in $\,J$)

An engine has an efficiency of $1/6$. When the temperature of the sink is reduced by $62^{\circ}C$,its efficiency is doubled. The temperature of the source is ....... $^{\circ}C$.