A cylinder with cross sectional area $0\mathrm{.}05m^2$ is fitted with a $300kg$ frictionless sliding piston. The cylinder initially contains a $0\mathrm{.}03m^3$ of an ideal gas with $C_v=21\mathrm{.}686k\frac{J}{k}$mol$-K$ at $\frac{20}{b}ar$ and $25C.$ Ambient pressure is $1$ bar. The piston is held in place by a pin in the cylinder. The pin is removed, and the piston very quickly rises $0\mathrm{.}6m$ until it hits a second pin and comes to a stop. What are the temperature and pressure of the gas and the velocity of the piston, just before it strikes the upper pin? You may want to use the differential form of the energy balance. $($ANS: $44\mathrm{.}5C,7\mathrm{.}65$ bar, $($:$14\mathrm{.}6\frac{m}{s}\}$