$A$ 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 $.......... \times 10^{6} \, J$.

The efficiency of a Carnot heat engine is $25 \%$ and the temperature of its source is $127^{\circ} C$. Without changing the temperature of the source,if the absolute temperature of the sink is decreased by $10 \%$,the new efficiency of the engine is: (in $\%$)

An ideal gas heat engine operates in a Carnot cycle between $227^{\circ}C$ and $127^{\circ}C$. It absorbs $6\,kcal$ at the higher temperature. The amount of heat (in $kcal$) converted into work is equal to

$A$ heat engine operating between temperatures $T_1$ and $T_2$ has an efficiency of $\frac{1}{6}$. When $T_2$ is lowered by $62 \ K$,its efficiency increases to $\frac{1}{3}$. Then $T_1$ and $T_2$ respectively are:

$A$ Carnot engine $A$ working between temperatures $600 \ K$ and $T$ $(T < 600 \ K)$ and another Carnot engine $B$ working between temperatures $T$ $(T > 400 \ K)$ and $400 \ K$ are connected in series. If the work done by both the engines is the same, then $T =$ (in $K$)

The efficiency of a Carnot engine operating with reservoir temperatures of $100\,^{\circ}C$ and $-23\,^{\circ}C$ will be