A given ideal gas with $\gamma = \frac{C_{p}}{C_{v}} = 1.5$ at a temperature $T$. If the gas is compressed adiabatically to one-fourth of its initial volume, the final temperature will be (1) $2\sqrt{2}\,T$ (2) $4T$ (3) $2T$ (4) $8T$
A given ideal gas with $\gamma = \frac{C_{p}}{C_{v}} = 1.5$ at a temperature $T$. If the gas is compressed adiabatically to one-fourth of its initial volume, the final temperature will be\\
(1) $2\sqrt{2}\,T$\\
(2) $4T$\\
(3) $2T$\\
(4) $8T$