March 12th, 2017, 12:27 PM  #1 
Newbie Joined: Dec 2015 From: England Posts: 27 Thanks: 0  Rearrangement of van der waals
Please could some one help me with question 7b

March 12th, 2017, 02:05 PM  #2 
Senior Member Joined: Jun 2015 From: England Posts: 662 Thanks: 187 
This is a simple substitution into the partial differential. Wherein lies the difficulty? 
March 12th, 2017, 02:19 PM  #3 
Senior Member Joined: Jun 2015 From: England Posts: 662 Thanks: 187 
$\displaystyle p = \frac{{nRT}}{{V  nb}}  a\frac{{{n^2}}}{{{V^2}}}$ $\displaystyle {\left( {\frac{{\partial p}}{{\partial T}}} \right)_V} = \frac{{nR}}{{V  nb}}  0$ $\displaystyle {\pi _T} = T{\left( {\frac{{\partial p}}{{\partial T}}} \right)_V}  p$ $\displaystyle {\pi _T} = T\left( {\frac{{nR}}{{V  nb}}} \right)  \left( {\frac{{nRT}}{{V  nb}}  a\frac{{{n^2}}}{{{V^2}}}} \right)$ $\displaystyle {\pi _T} = \frac{{TnR}}{{V  nb}}  \frac{{nRT}}{{V  nb}} + a\frac{{{n^2}}}{{{V^2}}} = a\frac{{{n^2}}}{{{V^2}}}$ as required 

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der, rearrangement, van, waals 
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