$A$ Carnot engine operates between $227^{\circ}C$ and $27^{\circ}C$. The efficiency of the engine will be:

Work done by a Carnot engine operating between temperatures $127^{\circ}C$ and $27^{\circ}C$ is $2\,kJ$. The amount of heat transferred to the engine by the source is $........\,kJ$.

An engine operating between the boiling and freezing points of water will have:
$1.$ Efficiency more than $27 \%$
$2.$ Efficiency less than the efficiency of a Carnot engine operating between the same two temperatures.
$3.$ Efficiency equal to $27 \%$
$4.$ Efficiency less than $27 \%$

$A$ 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:

$A$ Carnot engine takes $6000 \,cal$ of heat from a reservoir at $627^{\circ} C$ and gives it to a sink at $27^{\circ} C$. The work done by the engine is ......... $kcal$.