An ideal monatomic gas expands adiabatically from $0\mathrm{.}530$ m$3$ to $1\mathrm{.}63$ m$3.$ If the initial pressure and temperature are $1\mathrm{.}60105$ Pa and $345$ K$,$ respectively, find the number of moles in the gas, the final gas pressure, the final gas temperature, and the work done on the gas.An ideal monatomic gas expands adiabatically from $0\mathrm{.}530$ m$^3$ to $1\mathrm{.}63$ m$^3.$ If the initial pressure and temperature are $1\mathrm{.}6010^5$ Pa and $345$ K$,$ respectively, find the number of moles in the gas, the final gas pressure, the final gas temperature, and the work done on the gas.

the final gas temperature $($in K$)$