$A$ Carnot engine whose efficiency is $40 \%$, receives heat at $500 \ K$. If the efficiency is to be $50 \%$, the source temperature for the same exhaust temperature is (in $K$)

The efficiency of a Carnot engine operating between reservoirs maintained at temperatures $27^{\circ}C$ and $-123^{\circ}C$ is ...... $\%$

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

$A$ 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

An ideal Carnot heat engine has an efficiency of $30\%$. It absorbs heat from a hot reservoir at $727^{\circ}C$. The temperature of the cold reservoir is .... $^{\circ}C$.

Three Carnot engines operate in series between a heat source at temperature $T_1$ and a heat sink at a temperature $T_4$. There are two other reservoirs at temperatures $T_2$ and $T_3$. If the three engines are equally efficient,find the values of $T_2$ and $T_3$ in terms of $T_1$ and $T_4$,given that $T_1 > T_2 > T_3 > T_4$.