The following figure shows the $P-T$ graph for four processes $A, B, C,$ and $D$. Select the correct alternative.

The ratio of the specific heat capacities of a gas is $1.5$. When the gas undergoes an adiabatic process, its volume is doubled and its pressure becomes $P_1$. When the gas undergoes an isothermal process, its volume is doubled and its pressure becomes $P_2$. If $P_1 = P_2$, what is the ratio of the initial pressures of the gas when it undergoes adiabatic and isothermal processes?

Two gases $A$ and $B$ are filled at the same pressure in separate cylinders with movable pistons of radius $r_A$ and $r_B$,respectively. On supplying an equal amount of heat to both the systems reversibly under constant pressure,the pistons of gas $A$ and $B$ are displaced by $16 \ cm$ and $9 \ cm$,respectively. If the change in their internal energy is the same,then the ratio $\frac{r_A}{r_B}$ is equal to

$A$ monatomic gas of volume $V$ and pressure $P$ expands isothermally to a volume $27 V$ and then is compressed adiabatically to a volume $V$. The final pressure of the gas is: (in $P$)

An ideal gas undergoes four different processes from the same initial state as shown in the figure below. Those processes are adiabatic,isothermal,isobaric and isochoric. The curve which represents the adiabatic process among $1, 2, 3$ and $4$ is

In the $P-V$ diagram shown,the gas does $5 \, J$ of work in the isothermal process $ab$ and $4 \, J$ of work in the adiabatic process $bc$. What will be the change in internal energy of the gas in the straight path $c$ to $a$ (in $, J$)?