When a gas is compressed adiabatically by a piston in a cylinder,the work done on the gas is found to be $1.5 \times 10^{4} \, J$. During this process:

In an adiabatic expansion,the product of pressure and volume:

When air of the atmosphere rises up,it cools. Why?

If a gas of volume $400 \ cc$ at an initial pressure $P$ is suddenly compressed to $100 \ cc$,then its final pressure is (The ratio of the specific heat capacities of the gas at constant pressure and constant volume is $1.5$).

Two moles of an ideal monoatomic gas occupy a volume $V$ at $27^{\circ}C$. The gas expands adiabatically to a volume $2V$. Calculate $(a)$ the final temperature of the gas and $(b)$ the change in its internal energy.

$A$ cylinder with adiabatic walls is closed at both ends and is divided into two compartments by a frictionless adiabatic piston. Ideal gas is filled in both (left and right) compartments at the same $P, V, T$. Heating is started from the left side until the pressure changes to $\frac{27P}{8}$. If the initial volume of each compartment was $9 \text{ litres}$,then the final volume in the right-hand side compartment is . . . . . . litres. (for this ideal gas $\gamma = C_P/C_V = 1.5$)