$A$ Carnot engine has an efficiency of $\frac{1}{6}$. When the temperature of the sink is lowered by $57 \ K$,its efficiency becomes $\frac{1}{3}$. The temperature of the source is: (in $K$)

$A$ Carnot engine operating between temperatures $T_1$ and $T_2$ has an efficiency of $0.2$. When $T_2$ is lowered by $45 \text{ K}$, its efficiency becomes $0.5$. The temperatures $T_1$ and $T_2$ are respectively:

In a Carnot engine,the temperature of the reservoir is $527^{\circ} C$ and that of the sink is $200 \; K$. If the work done by the engine when it transfers heat from the reservoir to the sink is $12000 \; kJ$,the quantity of heat absorbed by the engine from the reservoir is $x \times 10^{6} \; J$. Find the value of $x$.

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

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:

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