The efficiency of a Carnot engine is found to increase from $25 \%$ to $40 \%$ on increasing the temperature $(T_1)$ of the source alone by $100 \ K$. The temperature $(T_2)$ of the sink is given by: (in $K$)

$A$ Carnot engine $C_1$ operates between temperatures $T_1$ and $T_2$ $(T_1 > T_2)$. $A$ second Carnot engine $C_2$ uses all the heat rejected by the engine $C_1$ and operates between temperatures $T_2$ and $T_3$ (where $T_2 > T_3$). The efficiency of this combined ($C_1$ and $C_2$ together) engine is

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

The first operation involved in a Carnot cycle is

$A$ Carnot engine operating between two reservoirs has an efficiency of $\frac{1}{3}$. When the temperature of the cold reservoir is raised by $x$,its efficiency decreases to $\frac{1}{6}$. The value of $x$,if the temperature of the hot reservoir is $99^{\circ} C$,will be $........ K$.

The temperature of the sink of a Carnot engine is $27^\circ C$. The efficiency of the engine is $25\%$. Then the temperature of the source is ...... $^\circ C$.