Hello,(adsbygoogle = window.adsbygoogle || []).push({});

I just need help deriving the fundamental equation from Equation of state for wan der waals fluids.

P=[itex]\frac{RT}{v-b}[/itex]-[itex]\frac{a}{v^2}[/itex]

and

u=cRT-[itex]\frac{a}{v}[/itex]

where a,b, and c are constants.

I know the fundamental equation is

dS=[itex]\frac{1}{T}[/itex]dU+[itex]\frac{P}{T}[/itex]dv

I solved the u equation so it's in terms of u and v and just plugged in the P equation to [itex]\frac{P}{T}[/itex] but then I get an equation of two variables which I am not sure how to integrate. So I get an equation in the form of

dS=f(u,v)dU + f(u,v)dv

Can someone help me with the integration please.

Thanks in advance!

**Physics Forums | Science Articles, Homework Help, Discussion**

Dismiss Notice

Join Physics Forums Today!

The friendliest, high quality science and math community on the planet! Everyone who loves science is here!

The friendliest, high quality science and math community on the planet! Everyone who loves science is here!

# Derive the fundamental equation from and equation of state

Can you offer guidance or do you also need help?

Draft saved
Draft deleted

**Physics Forums | Science Articles, Homework Help, Discussion**