$A$ Carnot engine has an efficiency of $50\%$ when its source is at a temperature $327^{\circ}C$. The temperature of the sink is $.........^{\circ}C$.

$A$ 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,

The efficiency of a Carnot heat engine is $25 \%$ and the temperature of its source is $127^{\circ} C$. Without changing the temperature of the source,if the absolute temperature of the sink is decreased by $10 \%$,the new efficiency of the engine is: (in $\%$)

$A$ Carnot engine converts $1/6$th of the heat into work. When the temperature of the sink is reduced by $62 \ K$,the efficiency of the engine is doubled. Calculate the temperatures of the source and the sink.

What is the efficiency of a heat engine? Write its formula.

The temperature of the sink of a Carnot engine is $300 \,K$ and the efficiency of the engine is $0.25$. If the temperature of the source of the engine is increased by $100 \,K$, the efficiency of the engine increases by: