Write expression for the work done by 1 mole of the gas in each of the following cases `:`
(i) For irreversible expansion of the gas from volume `V_(1)` to `V_(2)`.
(ii) For reversible isothermal expansion of the gas from volume `V_(1)` to`V_(2)`.
(iii)For expansion of the gas into an evaluated vessel.
(iv) For reversible isothermal compression of the gas from pressure `P_(1)` to `P_(2)`
(v)For adiabatic expansion resulting into change of temperature from `T_(1)` to `T_(2)`.

Explanation

(i)Irreversible expansion takes place when external pressure `(P_(ext))` remains constant
`w_("irrev")= - P_("ext") (V_(2)-V_(1))= -P_(ext) DeltaV`
(ii) Reversible expansion takes place when internal pressure is infinitesimally greater than exterhanl pressure `(P_("int")~=P_(ext))` at every stage. Thsu, externalpressurehas to be adjusted throughout.
`w_(rev)= -nRT ln. (V_(2))/(V_(1))`
(iii) The expansion is irreversible. Further, as `P_(ext) =0`, therefore,
`w= -P_(ext)DeltaV= 0 xx ( DeltaV) = 0`
(iv) When gas is compressed, work is done on the gas. For isothermal reversible compression,
`w= + nRT ln. (P_(2))/(P_(1))`
(v) For adiabatic expansion, temperature falls, i.e.,`T_(2) ltT_(1))`
`w=C_(v) (T_(2)-T_(1)),i.e., w` is -ve.