$A$ 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 $kJ$)

$A$ 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:

$A$ Carnot engine whose low temperature reservoir is at $7\,^{\circ}C$ has an efficiency of $50\%$. It is desired to increase the efficiency to $70\%$. By how many degrees should the temperature of the high temperature reservoir be increased? (in $K$)

Two Carnot engines $A$ and $B$ are operated in series. The first one,$A,$ receives heat at $T_1 = 600 \, K$ and rejects heat to a reservoir at temperature $T_2.$ The second engine $B$ receives the heat rejected by the first engine and,in turn,rejects heat to a reservoir at $T_3 = 400 \, K.$ Calculate the temperature $T_2$ if the work outputs of the two engines are equal. (in $K$)

In a Carnot engine,if the absolute temperature of the source is $25 \%$ more than the absolute temperature of the sink,then the efficiency of the engine is (in $\%$)

Two Carnot engines $A$ and $B$ operate in series such that engine $A$ absorbs heat $Q_1$ at temperature $T_1$ and rejects heat $Q$ to a sink at temperature $T$. Engine $B$ absorbs half of the heat rejected by engine $A$ (i.e.,$Q/2$) and rejects heat $Q_3$ to the sink at temperature $T_3$. When the work done in both cases is equal,the value of $T$ is: