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

An ideal gas goes through a reversible cycle $a\to b\to c\to d$ has the $V - T$ diagram shown below. Process $d\to a$ and $b\to c$ are adiabatic....  The corresponding $P - V$ diagram for the process is (all figures are schematic and not drawn to scale)

A cyclic process $ABCA$ is shown in $PT$ diagram. When presented on $PV$, it would

The volume of an ideal gas $(\gamma=1.5)$ is changed adiabatically from $5$ litres to $4$ litres. The ratio of initial pressure to final pressure is:

A monoatomic gas at pressure $P$ and volume $V$ is suddenly compressed to one eighth of its original volume. The final pressure at constant entropy will be $.....P$

Draw $P- V$ curves for isothermal and adiabatic processes of an ideal gas.