A gas is contained in a metallic cylinder fitted with a piston. The piston is suddenly moved in to compress the gas and is maintained at this position. As time passes, the pressure of the gas in the cylinder

Two samples of $A$ and $B$ are initially kept in the same state. The sample $A$ is expanded through an adiabatic process and the sample $B$ through an isothermal process up to the same final volume. The final pressures in $A$ and $B$ are $P_{\mathrm{A}}$ and $P_{\mathrm{B}}$ respectively. Then,

Four curves $A, B, C$ and $D$ are drawn in the figure for a given amount of gas. The curves which represent adiabatic and isothermal changes are

When an ideal gas undergoes an adiabatic change causing a temperature change $\Delta T$

(i) there is no heat gained or lost by the gas.
(ii) the work done by the gas is equal to a change in internal energy.
(iii) the change in internal energy per mole of the gas is $C_V\Delta T,$ where $C_V$ is the molar heat capacity at constant volume.