Two moles of an ideal monatomic gas at  ${127}^{0}C$  occupies a volume of V. If  the gas is expanded adiabatically to the volume 2V, then the work done by the gas will be $\left[\gamma =5/3,R=8.31J/molk\right]$

$T_2=T_1{\left(\frac{v_1}{v_2}\right)}^{r-1}$

                        $=400{\left(\frac{1}{2}\right)}^{2/3}$

                        $\frac{400}{2^{2/3}}$

                $T_2=252.0$

                $dw=\frac{nR\left(T_1-T_2\right)}{r-1}$

                $dw=\frac{2\times 8.3\left[400-252\right]}{\frac{2}{3}}$

                $dw=3685.2J$