$A$ reversible engine converts one-sixth of the heat supplied 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's heat engine works between the temperatures $427^{\circ} C$ and $27^{\circ} C$. How much heat in $kcal/s$ should it consume per second to deliver mechanical work at the rate of $1.0\,kW$?

$A$ 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 following figure shows a Carnot engine that works between temperatures $T_1=400 \text{ K}$ and $T_2=200 \text{ K}$ and drives a Carnot refrigerator that works between temperatures $T_3=350 \text{ K}$ and $T_4=250 \text{ K}$. The quantity $\frac{Q_3}{Q_1}$ will be

$A$ 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 cycle operating between $T_H = 600 \ K$ and $T_C = 300 \ K$ produces $1.5 \ kJ$ of mechanical work per cycle. The heat transferred to the engine by the reservoir is: (in $kJ$)