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March 12th, 2017, 12:27 PM   #1
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Rearrangement of van der waals

Please could some one help me with question 7b
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 March 12th, 2017, 02:05 PM #2 Senior Member   Joined: Jun 2015 From: England Posts: 915 Thanks: 271 This is a simple substitution into the partial differential. Wherein lies the difficulty? Thanks from topsquark
 March 12th, 2017, 02:19 PM #3 Senior Member   Joined: Jun 2015 From: England Posts: 915 Thanks: 271 $\displaystyle p = \frac{{nRT}}{{V - nb}} - a\frac{{{n^2}}}{{{V^2}}}$ $\displaystyle {\left( {\frac{{\partial p}}{{\partial T}}} \right)_V} = \frac{{nR}}{{V - nb}} - 0$ $\displaystyle {\pi _T} = T{\left( {\frac{{\partial p}}{{\partial T}}} \right)_V} - p$ $\displaystyle {\pi _T} = T\left( {\frac{{nR}}{{V - nb}}} \right) - \left( {\frac{{nRT}}{{V - nb}} - a\frac{{{n^2}}}{{{V^2}}}} \right)$ $\displaystyle {\pi _T} = \frac{{TnR}}{{V - nb}} - \frac{{nRT}}{{V - nb}} + a\frac{{{n^2}}}{{{V^2}}} = a\frac{{{n^2}}}{{{V^2}}}$ as required Thanks from topsquark and Andrzejku98

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