question_answer

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

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) \[nRT{{\log }_{e}}\left( \frac{{{V}_{2}}-n\beta }{{{V}_{1}}-n\beta } \right)+\alpha {{n}^{2}}\left( \frac{{{V}_{1}}-{{V}_{2}}}{{{V}_{1}}{{V}_{2}}} \right)\]

C) \[nRT{{\log }_{e}}\left( \frac{{{V}_{2}}-n\beta }{{{V}_{1}}-n\beta } \right)+\beta {{n}^{2}}\left( \frac{{{V}_{1}}-{{V}_{2}}}{{{V}_{1}}{{V}_{2}}} \right)\]

D) \[nRT{{\log }_{e}}\left( \frac{{{V}_{1}}-n\beta }{{{V}_{2}}-n\beta } \right)+\alpha {{n}^{2}}\left( \frac{{{V}_{1}}{{V}_{2}}}{{{V}_{1}}-{{V}_{2}}} \right)\]

Correct Answer: A

Solution :

According to given Vander Waal?s equation Work done,