Wednesday, September 20, 2017

gas laws - High pressure modification to the van der Waals equation


I get that a gas behaves non-ideally under high pressure and low temperature conditions. At high pressures, the density of a gas increases and attraction forces operate among molecules due to short intermolecular distance. This allows us to somehow modify the ideal gas equation. If a molecule is approaching the wall of container in order to collide, the neighbouring gas molecules soften their impact.


$$p_\text{ideal}=p_\text{real}+\frac{an^2}{V^2}$$


How was the term $\frac{an^2}{V^2}$ derived? My thoughts about that term, $\frac{n^2}{V^2}$ may be the extra pressure thats why the $V$ lies on the numerator (inverse relationship)




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