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

An engine takes in $5$ moles of air at $20\,^{\circ} C$ and $1$ $atm,$ and compresses it adiabaticaly to $1 / 10^{\text {th }}$ of the original volume. Assuming air to be a diatomic ideal gas made up of rigid molecules, the change in its internal energy during this process comes out to be $X\, kJ$. The value of $X$ to the nearest integer is

A sample of gas with $\gamma=1.5$ is taken through an adiabatic process in which the volume is compressed from $1200\, {cm}^{3}$ to $300\, {cm}^{3}$. If the initial pressure is $200\, {kPa}$. The absolute value of the workdone by the gas in the process $= \,….. J.$

One mole of helium is adiabatically expanded from its initial state $({P_i},{V_i},{T_i})$ to its final state $({P_f},{V_f},{T_f})$. The decrease in the internal energy associated with this expansion is equal to

A mixture of gases at $STP$ for which $\gamma=1.5$ is suddenly compressed to $\frac{1}{9}$ th of its original volume. The final temperature of mixture is ………. $^{\circ} C$