Worksheets/Van Der Waal Equation: Difference between revisions
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\dfrac{partial P}{\partial V} \bigg|_{T=T_c,V=V_c} = 0 | \dfrac{\partial P}{\partial V} \bigg|_{T=T_c,V=V_c} = 0 | ||
</math> | </math> | ||
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<math> | <math> | ||
\dfrac{partial^2 P}{\partial V^2} \bigg|_{T=T_c,V=V_c} = 0 | \dfrac{\partial^2 P}{\partial V^2} \bigg|_{T=T_c,V=V_c} = 0 | ||
</math> | </math> | ||
Revision as of 03:10, 22 May 2016
The Van Der Waal equation for a gas accounts for non-ideal behavior:
$ (P + \dfrac{a}{V^2})(V-b) = kT $
where P is the pressure, V is the molar volume (volume of a certain number of moles), a and b are constants that depend on the molecules, k is the Boltzmann constant, and T is temperature.
Now the critical points can be found: https://www.youtube.com/watch?v=VjVQxzxxLVw
Critical point is the saddle point of the above equation, and is defined as the point where:
$ \dfrac{\partial P}{\partial V} \bigg|_{T=T_c,V=V_c} = 0 $
and
$ \dfrac{\partial^2 P}{\partial V^2} \bigg|_{T=T_c,V=V_c} = 0 $