A gaseous sample is generally allowed to do only expansion/compression type of work against its surroundings. The work done in case of an irreversible expansion ( in the intermediate stages of expansion/ compression the states of gases are not defined). The work done can be calculated using dw=-P_("ext")dV while in case of reversible process the work done can be calculated using dw=-PdV where P is pressure of gas at some intermediate stages. Like for an isothermal reversible process, since P=(nRT)/(V),so, w=intdw=-int_(V_(i))^(V_(f))(nRT)/(V).dV=-nRT ""In((V_(f))/(V_(i))) Since,dw=PdV, so magnitude of work done can also be calculated by calculating the area under the PV curve of the reversible process in PV diagram. Two samples (initially under same states) of an idea gas are first allowed to expand to doubletheir volume using irreversible isothermal expansion against constant external pressure, then samples are turned back to their original volume first by reversible process having equation PV^(2)= constant then: