In which thermodynamic process is there no exchange of heat between the system and the surroundings?

$A$ diatomic gas undergoes adiabatic change. Its pressure $P$ and temperature $T$ are related as $P \propto T^{x}$ where the value of $x$ is

Helium at $27^oC$ has a volume of $8$ litres. It is suddenly compressed to a volume of $1$ litre. The temperature of the gas will be ....... $^oC$ $[\gamma = 5/3]$

The pressure $P_{1}$ and density $d_{1}$ of a diatomic gas $\left(\gamma = \frac{7}{5}\right)$ change suddenly to $P_{2} (> P_{1})$ and $d_{2}$ respectively during an adiabatic process. The temperature of the gas increases and becomes $......$ times its initial temperature. (Given $\frac{d_{2}}{d_{1}} = 32$)

Is it possible to increase the temperature of a gas without adding heat to it? Explain.

$A$ sample of $1$ mole of gas at temperature $T$ is adiabatically expanded to double its volume. If the adiabatic constant for the gas is $\gamma = \frac{3}{2}$,then the work done by the gas in the process is: