In a Carnot engine,when the temperatures are $T_2 = 0^{\circ} C$ and $T_1 = 200^{\circ} C$,its efficiency is $\eta_1$. When the temperatures are $T_1 = 0^{\circ} C$ and $T_2 = -200^{\circ} C$,its efficiency is $\eta_2$. Then the value of $\frac{\eta_1}{\eta_2}$ is:

Two Carnot engines $A$ and $B$ are operated in succession. The first one,$A$,receives heat from a source at $T_1 = 800 \ K$ and rejects heat to a sink at $T_2 \ K$. The second engine,$B$,receives the heat rejected by the first engine and rejects heat to another sink at $T_3 = 300 \ K$. If the work outputs of the two engines are equal,then the value of $T_2$ is .... $K$.

In a Carnot engine,the work done by the working substance is equivalent to:

$A$ 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:

$A$ reversible heat engine converts one-fourth of the heat input into work. When the temperature of the sink is reduced by $52 \, K$,its efficiency is doubled. The temperature in Kelvin of the source will be ...... .

$A$ Carnot's engine has an efficiency of $25 \%$ when its sink is at $27^{\circ} C$. If it has to be increased to $40 \%$,what should be the temperature of the sink keeping the temperature of the source constant (in $K$)?