Can a change in the internal energy of an ideal gas be considered an adiabatic process?

By what factor should the volume of an ideal gas $(\gamma = 1.5)$ be increased through an adiabatic expansion so that its $rms$ speed becomes half?

In an adiabatic process,the state of a gas is changed from $(P_1, V_1, T_1)$ to $(P_2, V_2, T_2)$. Which of the following relations is correct?

$A$ cycle tyre bursts suddenly. This process represents an:

The volume of a gas is reduced adiabatically to $(1/4)^{th}$ of its initial volume. If the initial temperature is $27\,^{\circ}C$ and $\gamma = 1.4$, the new temperature is:

$A$ rigid diatomic ideal gas undergoes an adiabatic process at room temperature. The relation between temperature and volume for the process is $TV^x =$ constant,then $x$ is