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:

- 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

Euler’s theorem says: !

Tricks with partials:

- Inversion
- Triple product
- Chain rule
- Maxwell’s reciprocity theorem:
- Jacobian: