$A$ Carnot engine takes $5000 \, kcal$ of heat from a reservoir at $727 \, ^{\circ}C$ and gives heat to a sink at $127 \, ^{\circ}C$. The work done by the engine is $.......... \times 10^{6} \, J$.

$A$ Carnot engine has the same efficiency between $800 \ K$ to $500 \ K$ and $x \ K$ to $600 \ K$. The value of $x$ is ...... $K$. (in $K$)

The efficiency of a Carnot engine is $50\%$ and the temperature of the sink is $500 \ K$. If the temperature of the source is kept constant and its efficiency is raised to $60\%$,then the required temperature of the sink will be: (in $K$)

The temperature-entropy $(T-S)$ diagram of a reversible engine cycle is given in the figure. Its efficiency is

Two ideal Carnot engines operate in cascade (all heat given up by one engine is used by the other engine to produce work) between temperatures $T_{1}$ and $T_{2}$. The temperature of the hot reservoir of the first engine is $T_{1}$ and the temperature of the cold reservoir of the second engine is $T_{2}$. $T$ is the temperature of the sink of the first engine,which is also the source for the second engine. How is $T$ related to $T_{1}$ and $T_{2}$,if both engines perform equal amounts of work?

If a Carnot engine works between $127^{\circ} C$ and $527^{\circ} C$,then its efficiency is ...... $\%$