Euler’s Theorem:

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



In thermo there are 2 special cases

1st detree in mass (extensive)

0th 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:


Euler’s theorem says: !









Tricks with partials:

  1. Inversion

  2. Triple product

  3. Chain rule

  4. Maxwell’s reciprocity theorem:






  5. Jacobian: