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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
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This is a simple substitution into the partial differential.

Wherein lies the difficulty?
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March 12th, 2017, 02:19 PM   #3
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$\displaystyle p = \frac{{nRT}}{{V - nb}} - a\frac{{{n^2}}}{{{V^2}}}$



$\displaystyle {\left( {\frac{{\partial p}}{{\partial T}}} \right)_V} = \frac{{nR}}{{V - nb}} - 0$



$\displaystyle {\pi _T} = T{\left( {\frac{{\partial p}}{{\partial T}}} \right)_V} - p$



$\displaystyle {\pi _T} = T\left( {\frac{{nR}}{{V - nb}}} \right) - \left( {\frac{{nRT}}{{V - nb}} - a\frac{{{n^2}}}{{{V^2}}}} \right)$



$\displaystyle {\pi _T} = \frac{{TnR}}{{V - nb}} - \frac{{nRT}}{{V - nb}} + a\frac{{{n^2}}}{{{V^2}}} = a\frac{{{n^2}}}{{{V^2}}}$


as required
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