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Pchem dump Rate Topic: -----

#1 4 November 2009 - 04:53 AM UC 


ydoaPs just lost the game
Start: dU=TdS-PdV

Divide across by dV and hold T constant.

(\frac{\partial U}{\partial V})_T=T(\frac{\partial S}{\partial V})_T-P

Use the maxwell relation (\frac{\partial P}{\partial T})_V=(\frac{\partial S}{\partial V})_T to get:


(\frac{\partial U}{\partial V})_T=T(\frac{\partial P}{\partial T})_V-P

Starting from PV=nRT , take the differential form and hold V constant:

d(PV)=d(nRT) \rightarrow VdP=nRdT \rightarrow (\frac{\partial P}{\partial T})_V=\frac{nR}{V}

Substitute that in to get:

(\frac{\partial U}{\partial V})_T=\frac{nRT}{V}-P

Simple rearrangement of the ideal gas law gives the value of the right side of that equation:

PV=nRT \rightarrow P=\frac{nRT}{V} \rightarrow 0=\frac{nRT}{V}-P

So, overall:

(\frac{\partial U}{\partial V})_T=0 [Valid only for ideal gases]
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#2 7 November 2009 - 04:57 AM Genecks 


Neuroscientist
I think PChem is evil, and we should eat it.
We should eat it for dinner.

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