In a Carnot engine,the temperature of the sink is $27 \, ^\circ C$ and the temperature of the source is $927 \, ^\circ C$. If the work done by the engine to reject heat from the source to the sink is $12.6 \times 10^{6} \, J$,what is the heat absorbed from the source?

$A$ Carnot engine with $40\%$ efficiency takes heat at $500 \ K$. If its efficiency is to be $50\%$,then for the same exhaust temperature,the intake temperature must 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,

$A$ frictionless heat engine can be $100 \%$ efficient only if its exhaust temperature is ............

The efficiency of a Carnot engine depends on what,and of what is it independent?

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 $27 \%$