Work done by a system under isothermal change from a volume \[{{V}_{1}}\] to \[{{V}_{2}}\] for a gas which obeys Vander Waal's equation \[(V-\beta n)\,\left( P+\frac{\alpha {{n}^{2}}}{V} \right)=nRT\]

• A.            \[nRT{{\log }_{e}}\left( \frac{{{V}_{2}}-n\beta }{{{V}_{1}}-n\beta } \right)+\alpha \,{{n}^{2}}\,\left( \frac{{{V}_{1}}-{{V}_{2}}}{{{V}_{1}}{{V}_{2}}} \right)\]
• B.            \[nRT{{\log }_{10}}\left( \frac{{{V}_{2}}-\alpha \beta }{{{V}_{1}}-\alpha \beta } \right)+\alpha \,{{n}^{2}}\,\left( \frac{{{V}_{1}}-{{V}_{2}}}{{{V}_{1}}{{V}_{2}}} \right)\]
• C.            \[nRT{{\log }_{e}}\left( \frac{{{V}_{2}}-n\alpha }{{{V}_{1}}-n\alpha } \right)+\beta \,{{n}^{2}}\,\left( \frac{{{V}_{1}}-{{V}_{2}}}{{{V}_{1}}{{V}_{2}}} \right)\]
• D.            \[nRT{{\log }_{e}}\left( \frac{{{V}_{1}}-n\beta }{{{V}_{2}}-n\beta } \right)+\alpha \,{{n}^{2}}\,\left( \frac{{{V}_{1}}{{V}_{2}}}{{{V}_{1}}-{{V}_{2}}} \right)\]