Starting at temperature 300 K , one mole of an ideal diatomic gas ( $\gamma=1.4$ ) is first compressed adiabatically from volume $V_1$ to $V_2=\frac{V_1}{16}$. It is then allowed to expand isobarically to volume $2 \mathrm{~V}_2$. If all the processes are the quasi-static then the final temperature of the gas (in ${ }^{\circ} \mathrm{K}$ ) is (to the nearest integer) $\_\_\_\_$ .