A certain quantity of an ideal gas is contained in a cylinder and occupies a volume of \(1.0 \mathrm{dm}^{3}\) at \(3 \mathrm{~atm}\) pressure. The gas is transferred by different paths to a final state where it occupies a volume of \(3.0 \mathrm{dm}^{3}\). The paths are mechanically reversible and the whole process takes place by the following two processes:

(i) an adiabatic expansion

(ii) an isothermal expansion to \(3.0 \mathrm{dm}^{3}\) followed by a change of pressure.

Calculate the work done of the gas, given that \(\gamma=1.4\).