What is constant in an adiabatic process?

During the adiabatic expansion of $2 \, moles$ of a gas,the internal energy was found to have decreased by $100 \, J$. The work done by the gas in this process is ..... $J$.

$A$ polyatomic gas $\left( \gamma = \frac{4}{3} \right)$ is compressed to $\frac{1}{8}$ of its volume adiabatically. If its initial pressure is $P_0$,its new pressure will be (in $P_0$)

One mole of an ideal gas expands adiabatically from $200 \,K$ to $250 \,K$. If the specific heat of the gas at constant volume is $0.8 \,kJ \,kg^{-1} \,K^{-1}$, then the work done by the gas is

$A$ polyatomic gas follows a law $T^2 V^\alpha = \text{constant}$. Find $\alpha$ for which the heat exchange of gas in the process becomes zero.

In an adiabatic process,if the pressure is increased by $\frac{2}{3}\% $ and the ratio of specific heats $\frac{C_p}{C_v} = \gamma = \frac{3}{2}$,then the volume decreases by about: