OUTLINE OF CHAPTER 6

Math Preliminaries

or

Extensive-intensive derivatives

Example: Extensive-extensive derivatives

Example:

More properties

Triple product rule

Chain rule

and for L=Z

EVALUATION OF THERMODYNAMIC PARTIAL DERIVATIVES

Definitions

Closed Systems

Then

Alternatively

But

Typo: should be at constant V, not constant T

ThendH dU VdP PdV TdS PdV VdP PdV TdS VdP= + + = − + + = + Or dividing by N

Similarly

Thus, directly from first law we get:

MAXWELL RELATIONS Expressions for other derivatives.

Then

Similarly

Expressions of S, U and H in terms of T and V or T and P (which are the convenient choices (why?)

But the Maxwell relation says

Then

Complete expressions of dU and dH in measurable entities

Substitute

to get

Similarly

IDEAL GAS AND ABSOLUTE TEMPERATURE SCALE

Starting point: PV and U are only functions of T

But

also

Therefore

Thus at constant V

Therefore

CHANGES OF THERMODYNAMIC PROPERTIES OF REAL

SUBSTANCES

We need a volumetric equation of state van del Waals

Redlich Kuong

Peng Robinson

Generalized Class

Virial

Benedict Webb Rubin

Heat Capacity We start from

Take P1=0 and V1=infinity

Enthalpy We start from

Integration paths

Alternative Path

Entropy Changes

Internal Energy Changes

Ideal Gases

DEPARTURE FUNCTIONS

where

PRINCIPLE OF CORRESPONDING STATES

Can we have ONE equation of state for all gases?

Assume van der Waals Gas

For the critical point:

Then

Solving

All van der Waal gases therefore have the same equation of state

Unfortunately not all gases have the same Zc

But, in general we can use a GRAPH!!!!