Derive a relation showing reversible work of expansion from volume `V_1` to `V_2` by 'n' moles of a real gas obeying van der waal's equation at temperature `T` where volume occupied by molecules may be taken as negligible in comparison to total volume of gas.

Explanation

For a real gas, `[P=(n^(2)a)/(V^(2))][V-nb]=nRT` if `nb lt lt V`, (as given),then
`[p+(n^(2)a)/(V^(2))]V=nRT`
or `P=(nRT)/V-(n^(2)a)/(V^(2))`
Now, work done in reversible expansion is
`w=-intPdV=-int_(V_(1))^(V_(2))(nRTdV)/V+int_(V_(1))^(V_(2))(n^(2)a)/(V^(2)).dV`
`=-nRT"log"(V_(2))/(V_(1))-[(n^(2)a)/(V_(2))-(n^(2)a)/(V_(1))]`
`=-nRT"log"(V_(2))/(V_(1))-n^(2)a[1/(V_(2))-1/(V_(1))]`