The first operation involved in a Carnot cycle is

$A$ 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 $K$)

What is the source temperature of the Carnot engine required to get $70 \%$ efficiency (in $^{\circ}C$)? Given sink temperature $= 27^{\circ}C$.

$A$ 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 $kJ$)

$A$ Carnot engine operating between temperatures $T_1$ and $T_2$ has an efficiency of $\frac{1}{6}$. When $T_2$ is lowered by $62\, K$,its efficiency increases to $\frac{1}{3}$. Then $T_1$ and $T_2$ are,respectively:

$A$ Carnot engine uses diatomic gas as a working substance. During the adiabatic expansion part of the cycle,if the volume of the gas becomes $32$ times its initial volume,then the efficiency of the engine is (in $\%$)