What is the efficiency of an ideal gas?

$A$ Carnot engine absorbs $3 \times 10^{6} \text{ cal}$ of heat from a reservoir at $627^{\circ}C$ and rejects it at $27^{\circ}C$. The work done by the engine is:

$A$ Carnot engine having efficiency $\frac{1}{6}$ operates between the source temperature $T_H$ and the sink temperature $T_C$. Its efficiency increases to $\frac{1}{3}$ when $T_C$ is decreased by $64 \text{ K}$. The temperatures $T_H$ and $T_C$ are respectively:

Efficiency of a heat engine whose sink is at temperature of $300 \,K$ is $40 \%$. To increase the efficiency to $60 \%$, keeping the sink temperature constant, the source temperature must be increased by (in $\,K$)

An ideal Carnot engine,whose efficiency is $40 \%$ receives heat at $500 \; K$. If its efficiency is $50 \%$ then the intake temperature for the same exhaust temperature is ......... $K$.

$A$ Carnot engine has an efficiency of $1/6$. When the temperature of the sink is reduced by $62\,^{\circ}C$,its efficiency is doubled. The temperatures of the source and the sink are,respectively: