# Proof for la grangian

1. ### georg gill

100
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

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. ### 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.

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