1. DICKY DERMAWAN www.dickydermawan.net78.net dickydermawan@gmail.com ITK-233 Termodinamika Teknik Kimia I 3 SKS 5 – Relations among Thermodynamic Properties & Properties Diagrams

2. State Principle The only measurable property is P, T & V How we can find U, H, S, … from this? We already have:

3. Fundamental Relations

4. Mathematical Formulation (1)

5. Mathematical Formulation (2) Elimination of the differential dy gives: Since dx and dz are independent, the coefficient of dx and dz must be zero, thus: and:

6. Fundamental Relations

7. Fundamental Properties & Maxwell Relations

8. Example H=H(T,P) a. How does enthalpy affected by temperature and pressure? b. Prove that c. Use the result of (a) to prove that enthalpy of ideal gas is affected only by temperature. d. State H=H(T,P) for virial gas: e. State H=H(T,P) for real gas:

9. Example: S=S(T,P) a. How does entropy affected by temperature and pressure? b. Prove that c. Show that for ideal gas

10. Example: U=U(T,V) a. How does internal energy affected by temperature and volume? b. Express the results of (a) in term of β and κ c. Use the result of (a) to prove that internal energy of ideal gas is not affected by pressure

11. Example: S=S(T,V) a. How does entropy affected by temperature and volume? b. Express the results of (a) in term of β and κ c. Show that for ideal gas with constant Cv:

12. Gibbs Energy as Generating Function a. Prove that b. c. d.

13. C p, C v & Pressure Effect The Joule-Thomson coefficient: is important in refrigeration engineering. Show that it can be calculated using: Prove that:

14. Example: U = U(T,P) a. Prove that b. Prove that the internal energy of ideal gas is not affected by pressure c. Prove that

15. Thermodynamic Property Diagrams Represents properties: P, V, T, H & S of a substance on a single plot. The most common: T/S Diagram P/H Diagram H/S (Mollier diagram)

16. T – S Diagram of Air

17. T – S Diagram of CO

18. T – S Diagram of CO2

19. P-H Diagram of Ammonia

20. P-H Diagram of Chlorine

21. H/S (Mollier Diagram) for NO

22. H/S (Mollier Diagram) for Water

23. Example 6.6 a. Superheated steam originally at 150 psia & 500 o F expands through a nozzle to an exhaust pressure of 50 psia. Assuming the process is reversible & adiabatic, determine the downstream state of the steam and ΔH. b. Repeat problem (a) if the process is irreversible with thermodynamic efficiency of 88%.