$300 \, cal$ 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 . . . . . . $^{\circ} C$.

Two Carnot engines $A$ and $B$ are operated in series. Engine $A$ receives heat from a reservoir at $600\,K$ and rejects heat to a reservoir at temperature $T$. Engine $B$ receives heat rejected by engine $A$ and in turn rejects it to a reservoir at $100\,K$. If the efficiencies of the two engines $A$ and $B$ are equal,what is the value of the intermediate temperature $T$ and the ratio of their efficiencies $\frac{\eta_A}{\eta_B}$?

Suppose that two heat engines are connected in series,such that the heat released by the first engine is used as the heat absorbed by the second engine,as shown in the figure. The efficiencies of the engines are $\epsilon_1$ and $\epsilon_2$,respectively. The net efficiency of the combination is given by:

An engine operating between temperatures $T_1$ and $T_2$ has efficiency $\eta = \frac{1}{5}$. When $T_2$ is lowered by $45 \ K$,its efficiency becomes $\eta' = \frac{1}{2}$. Temperatures $T_1$ and $T_2$ are respectively:

$A$ 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

What is the efficiency of a Carnot engine working between the boiling point and the freezing point of water (in $\%$)?