$A$ Carnot's engine operates with a source at $127^{\circ} C$ and a sink at $27^{\circ} C$. If the source supplies $40 \ kJ$ of heat energy,the work done by the engine is (in $kJ$)

The work done by a Carnot engine operating between $300 \,K$ and $400 \,K$ is $400 \,J$. The energy exhausted by the engine is (in $\,J$)

In the $1^{\text{st}}$ case,a Carnot engine operates between temperatures $300 \, K$ and $100 \, K$. In the $2^{\text{nd}}$ case,as shown in the figure,a combination of two engines is used. The efficiency of this combination (in the $2^{\text{nd}}$ case) will be:

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 .... $K$.

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:

The maximum possible efficiency of a heat engine is ...........