Use R=8.3 J/mol-K wherever required. Figure shows a cylindrical tube

Use $\mathrm{R}=8.3 \mathrm{~J} / \mathrm{mol}-\mathrm{K}$ wherever required.

Figure shows a cylindrical tube with adiabatic walls and fitted with a diathermic separator. The separator can be slid in the tube by an external mechanism. An ideal gas is injected in the two sides at equal pressures and equal temperatures. The separator remains in equilibrium at the middle. It is now solid to a position where it divides the tube in the ratio of $1: 3$. Find the ratio of the pressures in the two parts of the vessel.