Answer
3
Work Step by Step
$P_{i}V_{i}^{\gamma}=P_{f}V_{f}^{\gamma}$
Here, $i$ stands for initial and $f$ stands for final.
$P$ is pressure and $V$ is volume.
Given, $P_{f}=2P_{i}$
$\implies P_{i}V_{i}^{\gamma}=2P_{i}V_{f}^{\gamma}$
Or $V_{i}^{\gamma}=2V_{f}^{\gamma}$
Implies $(\frac{V_{i}}{V_{f}})^{\gamma}=2$
$\gamma=\frac{5}{3}$ gives
$(\frac{V_{i}}{V_{f}})^{\frac{5}{3}}=2$
Or $\frac{V_{i}}{V_{f}}=2^{\frac{3}{5}}=1.5$
Ratio of final volume to initial volume=
$\frac{V_{f}}{V_{i}}=3$
