Which of the following shows the correct relationship between the pressure $\text{'}P\text{'}$ and density $\rho$ of an ideal gas at constant temperature ?

Consider an ideal gas confined in an isolated closed chamber. As the gas undergoes an adiabatic expansion, the average time of collision between molecules increases as $V^{\mathrm{q}}$ , where $V$ is the volume of the gas. The value of $q$ is:

$\left(\gamma =\frac{{\mathrm{C}}_{\mathit{P}}}{{\mathrm{C}}_v}\right)$

Using equipartition of energy, the specific heat (in $\mathrm{J}\mathrm{ }{\mathrm{kg}}^{-1}\mathrm{ }{\mathrm{K}}^{-1}$ ) of Aluminium at high temperature can be estimated to be (atomic weight of Aluminium $=27$)