- #1
Matt atkinson
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Homework Statement
Considering entropy as a function of temperature and volume and using the Maxwell relation;
$$ \left(\frac{\partial S}{\partial V}\right)_T = \left(\frac{\partial p}{\partial T}\right)_V$$
Show that the entropy of a vessel is given by;
$$ S= R \left(\frac{3}{2}lnT+lnV+const\right) $$
Where R is the gas constant.
Homework Equations
Given in the question.
The Attempt at a Solution
So I made and attempt because S(T,V) you can write it as;
$$dS=\left(\frac{\partial S}{\partial V}\right)_T dV +\left(\frac{\partial S}{\partial T}\right)_V dT$$
Then substituted the maxwell relation;
$$dS=\left(\frac{\partial p}{\partial T}\right)_V dV + \left(\frac{\partial S}{\partial T}\right)_V dT$$
But from there I'm not sure where to go, i tried a few different things like dividing by dV but I'm drawing a blank, a nudge in the right direction would be appreciated.
Thanks in Advance.