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

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In summary, the joule expansion experiment can be explained using the first law of thermodynamics. At constant internal energy, the change in temperature with respect to volume is equal to zero. This can be shown by assuming that internal energy is a function of temperature for an ideal gas. By combining this with the equation of state, PV = k(T), it can be derived that the equation of state for an ideal gas is pV = RT, where R is a constant of proportionality.
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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.
 

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