All problems assume ideal gas $($IG$)$ behavior. $R=8\mathrm{.}3145Jmo{l}^{-1}{K}^{-1}=0\mathrm{.}082057Latmmo{l}^{-1}{K}^{-1}.$

Use J unit to report energies.

An IG initially occupying $5\mathrm{.}20L$ expands adiabatically, performing $1\mathrm{.}4kJ$ of work, the gas

worked against an external pressure of $1\mathrm{.}5$atm, reaching this pressure at the final

equilibrium state. The final temperature is $200K.$ What is the number of mols of the gas?