What is the efficiency of an ideal gas?

Temperature of a cold reservoir of a Carnot engine is $127^{\circ} C$. If the efficiency of the Carnot engine is $20 \%$,then the temperature of the hot reservoir is (in $^{\circ} C$)

An ideal heat engine working between temperatures $T_1$ and $T_2$ has an efficiency $\eta$. What will be the new efficiency if both the source and sink temperatures are doubled?

Three Carnot engines operate in series between a heat source at a temperature $T_1$ and a heat sink at temperature $T_4$ (see figure). There are two other reservoirs at temperatures $T_2$ and $T_3$,as shown,with $T_1 > T_2 > T_3 > T_4$. The three engines are equally efficient if

For an ideal heat engine,the temperature of the source is $127\,^{\circ} C$. In order to have $60\, \%$ efficiency,the temperature of the sink should be $........\,{ }^{\circ} C$. (Round off to the nearest integer)

$A$ 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 $kJ$)