One mole of a diatomic gas undergoes a process $P=\frac{P_0}{\left[1+{\left({\displaystyle \frac{V}{V_0}}\right)}^3\right]}$ where $P_0$ and $V_0$ are constants. The translational kinetic energy of the gas when $V=V_0$ is given by

In the diagram as shown, find parameters representing $x$ and $y$ axes and also parameter $Z$, if $Z_1=Z_2,Z_3=Z_4$ and $Z_2>Z_3$.

A $P-T$ diagram is shown below. Choose the corresponding $V-T$ diagram.

For process, $1$ $\mathrm{\Delta }\mathrm{U}$ is positive, for process $2$, $\mathrm{\Delta }U$ is zero and for process $3$, $\mathrm{\Delta }U$ is negative. Find the parameters indicating $x$ and $y$ axes.

$1$ mole of an ideal gas is contained in a cubical box of volume $\mathrm{V}$, $\mathrm{ABCDEFGH}$ at $300 \mathrm{K}$ (figure). One face of the box $\left(\mathrm{EFGH}\right)$ is made up of a material which totally absorbs any gas molecule incident on it.

At any given time,

An experiment is carried on a fixed amount of gas at different temperatures and at high pressure such that it deviates from the ideal gas behaviour. The variation of $\frac{\mathrm{PV}}{\mathrm{RT}}$ with $\mathrm{P}$ is shown in the diagram. The correct variation will correspond to