1. ChemE 260 Entropy Generation Fundamental Property Relationships May 6, 2005 Dr. William Baratuci Senior Lecturer Chemical Engineering Department University of Washington TCD 7: C & D CB 6: 2, 7 & 9

2. Principle of Increasing Entropy Clausius: Apply to Cycle 1-A-2-B Introduce Entropy: Substitute into Clausius: Rearrange: Differential Form: Baratuci ChemE 260 May 6, 2005

3. Entropy Generation Newest Statement of the 2 nd Law : Baratuci ChemE 260 May 6, 2005 Make Clausius into an equality: Entropy Generation, S gen –Internally reversible processes: –Irreversible processes: –Impossible processes:

4. TS Diagram Area under the curve: But: Irreversible Processes: S gen is a path variable ! We must use : Baratuci ChemE 260 May 6, 2005

5. Isolated Systems Entropy Statement of the 2 nd Law: Isolated Systems,  Q = 0, therefore: The universe is an isolated system: The Principle of Increasing Entropy (a consequence of the 2 nd 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: Boundary work for an internally reversible process: 1 st Gibbs Equation: Definition of enthalpy: Substitute in the 1 st Gibbs Eqn: 1 st Law, closed system, W b only: 2 nd 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 Definition: Relationship with Shomate Eqn : Where T ref is the reference temperature at which S = 0. 1 st Gibbs Eqns for ideal gases : Substitute the Ideal Gas Entropy Function : Baratuci ChemE 260 May 6, 2005

11. Ideal Gas Entropy Function Definition: Relationship with Shomate Eqn : Where T ref is the reference temperature at which S = 0. 2 nd 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