Two Carnot engines $A$ and $B$ are operated in series. The engine $A$ receives heat from the source at temperature $T_1$ and rejects the heat to the sink at temperature $T$. The second engine $B$ receives the heat at temperature $T$ and rejects to its sink at temperature $T_2$. For what value of $T$ the efficiencies of the two engines are equal?

Initial pressure and volume of a gas are $P$ and $V$ respectively. First it is expanded isothermally to volume $4\ V$ and then compressed adiabatically to volume $V.$ The final pressure of gas will be (given $\gamma = 3/2)$

An ideal gas undergoes a thermodynamics cycle as shown in figure. Which of the following graphs represents the same cycle?

$P-V$ plots for two gases during adiabatic process are shown. Plots $(1)$ and $(2)$ corresponds to

In the following indicator diagram, the net amount of work done will be

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