At $27^{o}C$ a gas is compressed suddenly such that its pressure becomes ($\dfrac{1}{8}$)th of original pressure. Final temperature will be ($\gamma$ = 5/3)

$\frac{T_{2}}{T_{1}}=\left(\frac{P_{2}}{P_{1}}\right)^{\frac{\gamma-1}{\gamma}}$

bstitute the given values:

$\frac{T_{2}}{300}=\left(\frac{1}{8}\right)^{\frac{5 / 3-1}{5 / 3}}=\left(\frac{1}{8}\right)^{\frac{2}{5}}$

w calculate $\left(\frac{1}{8}\right)^{\frac{2}{5}}$ :

$\begin{array}{c} \left(\frac{1}{8}\right)^{\frac{2}{3}}=0.435 \\ \frac{T_{2}}{300}=0.435 \\ T_{2}=0.435 \times 300=130.06.12 \mathrm{~K} \end{array}$

ep 2: Convert final temperature back to Celsius:

$T_{2}=130.6 \mathrm{~K}-273=-142.4^{\circ} \mathrm{C}$