$A$ gas at normal temperature is suddenly compressed to one-fourth of its original volume. If $\frac{C_{p}}{C_{v}}=\gamma=1.5$,then the increase in its temperature is (in $K$)

$A$ given ideal gas with $\gamma = \frac{C_p}{C_v} = 1.5$ is at a temperature $T$. If the gas is compressed adiabatically to one-fourth of its initial volume,the final temperature will be ..... $T$.

One mole of nitrogen gas being initially at a temperature of $T_0 = 300 \,K$ is adiabatically compressed to increase its pressure $10$ times. The final gas temperature after compression is (Assume, nitrogen gas molecules as rigid diatomic and $100^{1/7} = 1.9$) (in $\,K$)

Which of the following is true in the case of an adiabatic process, where $\gamma = C_p / C_V$?

Does the internal energy of an ideal gas change in an adiabatic process?

One mole of an ideal gas with $\gamma = 1.4$ is adiabatically compressed so that its temperature rises from $27^{\circ}C$ to $35^{\circ}C$. The change in the internal energy of the gas is ....... $J$ $(R = 8.3 \, J/mol \cdot K)$.