ChemE 260 Entropy Generation Fundamental Property Relationships

1
ChemE 260 Entropy GenerationFundamental
Property Relationships

• Dr. William Baratuci
• Senior Lecturer
• Chemical Engineering Department
• University of Washington
• TCD 7 C DCB 6 2, 7 9

May 6, 2005
2
Principle of Increasing Entropy

• Clausius

• Apply to Cycle 1-A-2-B

• IntroduceEntropy

• Substitute into Clausius

• Rearrange

• Differential Form

Baratuci ChemE 260 May 6, 2005
3
Entropy Generation

• Newest Statement of the 2nd Law

• Make Clausius into an equality

• Entropy Generation, Sgen
• Internally reversible processes
• Irreversible processes
• Impossible processes

Baratuci ChemE 260 May 6, 2005
4
TS Diagram

• Area underthe curve

• But

• Irreversible Processes

• Sgen is a path variable ! We must use

Baratuci ChemE 260 May 6, 2005
5
Isolated Systems

• Entropy Statement of the 2nd Law

• Isolated Systems, ?Q 0, therefore

• The universe is anisolated system

The Principle of Increasing Entropy(a
consequence of the 2nd Law)

• Divide the universe into two regions
• The system and the surroundings

Baratuci ChemE 260 May 6, 2005
6
The Gibbs Equations

• Definition of entropy

• 1st Law, closed system, Wb only

• Boundary work for an internally reversible
  process

• 1st Gibbs Equation

• Definition of enthalpy

• Substitute in the 1st Gibbs Eqn

• 2nd Gibbs Eqn

Baratuci ChemE 260 May 6, 2005
7
Incompressible Liquids

• Assumptions

• Gibbs Equations

• Enthalpy, internal energy and heat capacity

• Result

Baratuci ChemE 260 May 6, 2005
8
Ideal Gases

• Gibbs Equations

• Ideal Gas Heat Capacities and EOS

• Integration yields

Baratuci ChemE 260 May 6, 2005
9
Using the Shomate Equation

• This method is accurate for ideal gases, but it
  is tedious.

Baratuci ChemE 260 May 6, 2005
10
Ideal Gas Entropy Function
Where Tref is the reference temperature at which
S 0.

• Definition

• Relationship with Shomate Eqn

• 1st Gibbs Eqns for ideal gases

• Substitute the Ideal Gas Entropy Function

Baratuci ChemE 260 May 6, 2005
11
Ideal Gas Entropy Function
Where Tref is the reference temperature at which
S 0.

• Definition

• Relationship with Shomate Eqn

• 2nd Gibbs Eqns for ideal gases

• Substitute the Ideal Gas Entropy Function

Baratuci ChemE 260 May 6, 2005
12
Next Class

• Polytopic Processes P V? C
• More to this type of process than meets the eye
• Determination of Boundary Work
• PV Diagrams Revisited !
• Isentropic Processes
• A special case of the polytropic process
• The Relative Property Method of analysis

Baratuci ChemE 260 May 6, 2005