The Carnot cycle is plotted on a $P-V$ graph. Which portion represents an isothermal expansion?

$A$ Carnot engine is made to work between $200^{\circ}C$ and $0^{\circ}C$ first and then between $0^{\circ}C$ and $-200^{\circ}C$. The ratio of efficiencies of the engine in the two cases is

$A$ Carnot engine converts $1/6$th of the heat into work. When the temperature of the sink is reduced by $62 \ K$,the efficiency of the engine is doubled. Calculate the temperatures of the source and the sink.

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

$A$ reversible Carnot heat engine converts $\frac{1}{4}$ of its input heat into work. When the temperature of the sink is reduced by $50 \ K$,its efficiency becomes $33 \frac{1}{3} \%$. The initial temperatures of the source and the sink respectively are