A diatomic gas (considered to be an ideal gas) with rotational and vibrational degrees of freedom is confined in a cylindrical container with a movable piston. The gas is adiabatically compressed to half of its initial volume. If the ratio of the specific heat capacities for the gas is 7/5, what is the final temperature of the gas in terms of its initial temperature
1
\( T_f = T_0 \times 2^{\frac{2}{7}} \)
2
\( T_f = T_0 \times 2^{\frac{2}{5}} \)
3
\( T_f = T_0 \times 2^{\frac{7}{5}} \)
4
\( T_f = T_0 \times 2^{\frac{5}{2}} \)