The internal energy of a gas will increase when it

The pressure and density of a diatomic gas $(\gamma = 7/5)$ change adiabatically from $(P, d)$ to $(P', d')$. If $\frac{d'}{d} = 32$,then $\frac{P'}{P}$ is equal to:

One mole of an ideal gas at an initial temperature of $T \ K$ does $6R \ J$ of work adiabatically. If the ratio of specific heats of this gas at constant pressure and at constant volume is $5/3$,the final temperature of the gas will be:

$A$ gas $(\gamma = 1.3)$ is enclosed in an insulated vessel fitted with an insulating piston at a pressure of $10^5 \ N/m^2$. On suddenly pressing the piston,the volume is reduced to half the initial volume. The final pressure of the gas is:

Assertion $(A)$: When an ideal gas is compressed adiabatically,its temperature and the average kinetic energy of the gas molecules increase.
Reason $(R)$: The kinetic energy increases because of collisions of molecules with the moving parts of the wall.

What is an adiabatic process? Derive an expression for work done in an adiabatic process.