# Proof for la grangian

1. Feb 5, 2012

### georg gill

As this thread implies i wanted to try to prove ideal gas equation pV=vnRT

where T is tempearture p is pressure n is mole V is volume and R is gas constant

and then I found that I had to prove la grangian

What I wonder about is given in thread here

https://www.physicsforums.com/showthread.php?t=574248

In the end of the thread it is said that someone her might be able to help me with a suitable textbook. Is that possible?

2. Feb 5, 2012

### Studiot

Hello Georg,

As with strangerep in the other thread you started I am not sure what you are attempting, but you should look up the Joule experiment and the Joule-Thompson experiment.

They proved experimentally that the so called internal pressure of an ideal gas is zero.

This provides an alternative definition of an ideal gas as a gas with

$${\left( {\frac{{\partial U}}{{\partial V}}} \right)_T} = 0$$

You can use this plus Boyle's law to derive PV=NRT.

The following thermodynamic relation is also useful. this relates to all substances, not only ideal gasses.

$${\left( {\frac{{\partial U}}{{\partial V}}} \right)_T} + P = T{\left( {\frac{{\partial P}}{{\partial T}}} \right)_V}$$

By the way did you see my answer in your other thread about reversibility?

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