One mole of an ideal gas undergoes a linear process as shown in the figure below. Its temperature expressed as a function of volume $V$ is

Select the correct statement.

Initially,a gas of diatomic molecules is contained in a cylinder of volume $V_{1}$ at a pressure $P_{1}$ and temperature $250\, K$. Assuming that $25\%$ of the molecules get dissociated,causing a change in the number of moles. The pressure of the resulting gas at temperature $2000\, K$,when contained in a volume $2V_{1}$,is given by $P_{2}$. The ratio $\frac{P_{2}}{P_{1}}$ is:

Which of the following graphs represents the variation of $\beta = -(dV/dP)$ with pressure $P$ for an ideal gas kept at a constant temperature?

$A$ certain amount of an ideal gas is contained in a closed vessel. The vessel is moving with a constant velocity $v$. The molecular mass of the gas is $M$. What is the rise in temperature of the gas when the vessel is suddenly stopped? (Given $\gamma = C_P/C_V$)

From a certain apparatus,the diffusion rate of hydrogen has an average value of $28.7 \; cm^3 s^{-1}$. The diffusion of another gas under the same conditions is measured to have an average rate of $7.2 \; cm^3 s^{-1}$. Identify the gas.