P$2\mathrm{.}15$ A bottle at $325K$ contains an ideal gas at a pressure of $162\mathrm{.}5{10}^{3}Pa.$ The rubber stopper closing the bottle is removed. The gas expands adiabatically against $P_{\text{e}\text{x}\text{t}\text{e}\text{r}\text{n}\text{a}\text{l}}=120\mathrm{.}0{10}^{3}Pa,$ and some gas is expelled from the bottle in the process. When $P=P_{\text{e}\text{x}\text{t}\text{e}\text{r}\text{n}\text{a}\text{l}},$ the stopper is quickly replaced. The gas remaining in the bottle slowly warms up to $325K.$ What is the final pressure in the bottle for a monatomic gas, for which $1-,C_{V,m}=3\frac{R}{2},$ and a diatomic gas, for which $C_{V,m}=5\frac{R}{2}?$