The efficiency of a Carnot engine,working between the steam point and the ice point,will be $....\,\%$ (in $.81$)

$A$ Carnot engine whose efficiency is $40 \%$,receives heat at $500 \ K$. If the efficiency is to be $50 \%$,the source temperature for the same exhaust temperature is (in $K$)

$A$ Carnot engine whose heat sink is at $27^{\circ} C$ has an efficiency of $40 \%$. By how much should its source temperature be changed so as to increase its efficiency to $60 \% (in $K$)?$

An ideal heat engine exhausting heat at $77^{\circ}C$ is to have a $30\%$ efficiency. It must take heat at ...... $^{\circ}C$.

$A$ Carnot's engine operates with a source at $127^{\circ} C$ and a sink at $27^{\circ} C$. If the source supplies $40 \ kJ$ of heat energy,the work done by the engine is (in $kJ$)

The temperature of the source of a Carnot engine operating with an efficiency of $70\%$ is $1000 \ K$. The temperature of its sink is ...... $K$.