Euler’s Theorem:

For a homogeneous function to degree n in x + y:

If

Then

In thermo there are 2 special cases

1^st detree in mass (extensive)

0^th degree in mass (intensive)

In general:

For energy:

1. becomes:

\ U is a single value state function.

Corollary – Postulate 1:

Any intensive variable can be expressed as n + 1 independent intensive variables.

N.B. = intensive & extensive variable derivatives have different meanings.

We showed earlier:

Since

Tricks with partials:

1. Inversion

   

2. Triple product

   

3. Chain rule

   

4. Maxwell’s reciprocity theorem:

   

   

    

    

    

    

    

5. Jacobian: