Question

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 $(V-\beta n)(P+\frac{\alpha n^2}{V})=nRT$

• A.
• B.
• C.
• D.

Answer 1

The correct option is A

According to given Vander Waal's equation

$P=\frac{nRT}{V-n\beta }-\frac{a{n}^2}{V^2}$

Work done,

$W={\int }_{V_1}^{V_2}PdV=nRT{\int }_{V_1}^{V_2}\frac{dV}{V-n\beta }-\alpha n^2{\int }_{V_1}^{V_2}\frac{dV}{V^2}$

= $nRT\left[lo{g}_e\right(V-n\beta ){]}_{V_1}^{V_2}+\alpha n^2{\left[\frac{1}{V}\right]}_{V_1}^{V_2}$

= $nRTlo{g}_e\frac{V_2-n\beta }{V_1-n\beta }+\alpha n^2\left(\frac{V_1-V_2}{V_1{V}_2}\right)$