Understanding Joule Expansion and Its Implications on (dT/dV) const U = 0

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Homework Statement



\"Explain why the joule expansion experiment implies that (dT/dV) const U = 0\"


Homework Equations





The Attempt at a Solution



So I\'m not sure how to do this!

Using 1st law we can say that at const U Tds = pdV, but not sure how to get what they want..
 
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Ok so i guess you can just say that U = U(T) for an ideal gas...then the result follows.

The next part asks me to show that that equation i.e. (dT/dV) const U = 0 and the equation PV = k(T) --i.e. pV = some function of T, together imply the equation of state is pV = RT where R is some constant of proportionality..

How is this meant to work? Thanks.