$A$ 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 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,

$300 \, cal$ of heat is given to a heat engine and it rejects $225 \, cal$ of heat. If the source temperature is $227^{\circ} C$,then the temperature of the sink will be . . . . . . $^{\circ} C$.

What is the source temperature of the Carnot engine required to get $70 \%$ efficiency (in $^{\circ}C$)? Given sink temperature $= 27^{\circ}C$.

$A$ Carnot engine operates between two reservoirs of temperatures $900 \; K$ and $300 \; K$. The engine performs $1200 \; J$ of work per cycle. The heat energy (in $J$) delivered by the engine to the low-temperature reservoir in a cycle is:

$A$ 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: