CHEE2325 Thermodynamics Lecture 6 Summary

CHEE2325 – Lecture 6


Fundamental relationships:
- An EOS relates fundamental thermodynamic properties. It can be combined
with other relations to calculate other thermodynamic properties. For example:
^ )= RT − a
P=f ( T , V
V^ −b V ^2
- Typically, internal energy is expressed as a function of temperature and
volume, and enthalpy is expressed as a function of temperature and pressure.

- For a function z=f ( x , y ): dz=
∂z
∂x y
dx+
∂z
∂y x ( ) ( )
dy

- Rearranging and combining equations from previous lectures, we get:

( ) ( ) ( ) ( )
∂U ^ ∂U^ ∂^H ∂^ H
=T =−P =T ^
=V
^
∂ S V^ ^
∂ V S^ ^
∂S P ∂ P S^
- The maxwell relations relate partial derivatives of fundamental properties:

( ) ( )( ) ( )( ) ( ) ( ) ( )
∂P ∂T ∂V ^ ∂T ∂ ^S ∂P ∂ ^S ∂ V^
− = = = − =
∂ ^S V^ ∂ V^ ^S ∂ ^S V^ ∂ P S^ ∂ V
^ T ∂ T V^ ∂ P T ∂ T P
- There are also maxwell relations and thermodynamic identities for Helmholtz
free energy and Gibbs free energy.
- General relations for thermodynamic properties are given below:

^ =∫ CV dT +∫ T
∆U
(( ) )
∂P
∂T V^
^∆ H
−P d V
∂T
^
^ −T ∂ V
^ =∫ C P dT +∫ V
( ( )) P
dP


∆ S^ =∫
CP
T
dT +∫
^
∂V
∂T ( ) dP
P




Departure functions:
- The departure (residual) function is the difference between the value of a
property of a gas at its real state, and its ideal gas state.
^
M =M ^ ig + ^
M
dep


- We can find properties of a real fluid by finding the ideal gas and departure
properties.
- Departure functions are given by:

( )
^


( ) ( ( ∂T ) ) ^
T,P T ,V
^
^
H dep ( T , P )= ∫ ^ −T ∂ V
V ^ ( T , P )= ∫ T ∂ P −P d V
dPU dep

T , P=0
∂T P ^ =∞
T ,V V^



(( ∂∂ V^T ) − RP ) dP
T,P
^S ( T , P )= ∫
dep

T , P=0 P