Chapter 2, Problem 2.15NP

A bottle at 325 K contains an ideal gas at a pressure of $\text{162}.\text{5}\times \text{1}{0}^{\text{3}}\text{Pa}$. The rubber stopper closing the bottle is removed. The gas expands adiabatically against ${\text{P}}_{external}=\text{12}0.0\times \text{1}{0}^{\text{3}}\text{Pa}$, and some gas is expelled from the bottle in the process. When $P=P_{external}$, the stopper is quickly replaced. The gas remaining in the bottle slowly warms up to 325 K. What is the final pressure in the bottle for a monatomic gas, for which $C_{v,m}=3R/2$, and a diatomic gas, for which $C_{v,m}=5R/2$?