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

$A$ Carnot cycle for a gas is represented in the pressure-volume $(P-V)$ diagram shown below. Consider the following statements:
$I.$ The area of $ABCD$ is the work done by the gas.
$II.$ The area of $ABCD$ is the total heat absorbed.
$III.$ The change in internal energy of the cycle is zero.
Which of the following is correct?

In thermodynamic processes, which of the following statements is not true?

Given below are two statements:
Statement $I:$ If heat is added to a system,its temperature must increase.
Statement $II:$ If positive work is done by a system in a thermodynamic process,its volume must increase.
In the light of the above statements,choose the correct answer from the options given below.

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

$A$ certain amount of gas is taken through a cyclic process $(A-B-C-D-A)$ that has two isobars, one isochore, and one isothermal process. The cycle can be represented on a $P-V$ indicator diagram as: