[QUE/SM-02002] SM-PROBLEM

A thermally insulated chamber contains $1000$ moles of mono-atomic ideal gas\footnote{$PV=nRT$} at $10$ atm. pressure. Its temperature is $300$ K. The gas leaks out slowly through a valve into the atmosphere. The leaking process is quasi static, reversible and adiabatic \(^\)1

1. How many moles of gas shall be left in the chamber eventually?
2. What shall be the temperature of the gas left in the chamber ?

$1$ atm $=0.981\times 10^6$ Pa ; $\gamma={\displaystyle \frac{C_P}{C_V}=\frac{5}{3}}$ .       

Footnote 1 :: $PV^\gamma=\Theta$ where $\Theta$ is a constant.}.                                        KPN