The efficiency of a Carnot heat engine is $0.5$ when the temperature of the source is $T_{1}$ and that of the sink is $T_{2}$. The efficiency of another Carnot heat engine is also $0.5$. The temperatures of the source and sink of the second engine are respectively:

Even a Carnot engine cannot give $100\%$ efficiency because we cannot

$A$ Carnot engine with efficiency $\eta$ operates between two heat reservoirs with temperatures $T_1$ and $T_2$, where $T_1 > T_2$. If only $T_1$ is changed by $0.4 \%$, the change in efficiency is $\Delta \eta_1$, whereas if only $T_2$ is changed by $0.2 \%$, the efficiency is changed by $\Delta \eta_2$. The ratio $\frac{\Delta \eta_1}{\Delta \eta_2}$ is approximately,

$A$ reversible engine converts one-sixth of the heat input into work. When the temperature of the sink is reduced by $62^\circ C$,the efficiency of the engine is doubled. The temperatures of the source and sink are:

In a Carnot engine,if the work done during isothermal expansion is $25 \%$ more than the work done during isothermal compression,then the efficiency of the engine is: (in $\%$)

$A$ diatomic gas is used in a Carnot heat engine. If the efficiency of the given Carnot heat engine is $80\%$,then find the ratio of the initial volume to the final volume of the gas during adiabatic expansion.