$A$ Carnot heat engine works with an ideal diatomic gas and an adiabatic volume expansion ratio of $32$. Then its efficiency is ....... $\%$

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?

$A$ Carnot engine has an efficiency of $40\%$. The temperature of its sink is $300 \ K$. To increase the efficiency by $50\%$ of its original efficiency while keeping the sink temperature constant,by how many $K$ must the source temperature be increased?

$A$ 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 operating between temperatures $7^{\circ}C$ and a higher temperature has an efficiency of $50\%$. To increase its efficiency to $70\%$,by how much must the temperature of the source be increased in $K$?