$A$ Carnot heat engine has an efficiency of $20 \%$. The energy is supplied to the engine at the rate of $2 \text{ kW}$. The output power of the engine is (in $\text{ W}$)

$A$ 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 whose sink is at $300 \, K$ has an efficiency of $50 \%$. By how much should the temperature of the source be increased so that the efficiency becomes $70 \%$?

$A$ Carnot engine absorbs $1000\,J$ of heat energy from a reservoir at $127\,^oC$ and rejects $600\,J$ of heat energy during each cycle. The efficiency of the engine and the temperature of the sink will be:

$A$ heat engine operates between a cold reservoir at temperature $T_{2} = 400 \, K$ and a hot reservoir at temperature $T_{1}$. It takes $300 \, J$ of heat from the hot reservoir and delivers $240 \, J$ of heat to the cold reservoir in a cycle. The minimum temperature of the hot reservoir has to be $.... K$.

$A$ 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,