2. Thermo & Stat Mech - Spring 2006 Class 8 1 Thermodynamics and Statistical Mechanics Thermodynamic Potentials

3. Thermo & Stat Mech - Spring 2006 Class 82 Thermodynamic Potentials There are two energy functions that have been used so far: Internal Energy Enthalpy There are two more.

4. Thermo & Stat Mech - Spring 2006 Class 83 Properties From first law: TdS = dU + PdV, or Internal Energy dU = TdS – PdV U(S, V) Enthalpy: H = U + PV dH = TdS + VdP H(S, P)

5. Thermo & Stat Mech - Spring 2006 Class 84 New Potentials Helmholtz Function: F = U – TS Gibbs Function: G = U – TS + PV G = H – TS G = F + PV

6. Thermo & Stat Mech - Spring 2006 Class 85 Properties Helmholtz Function: F = U – TS dF = dU – TdS – SdT First Law: dU = TdS – PdV dF = – PdV – SdT F(V, T)

7. Thermo & Stat Mech - Spring 2006 Class 86 Properties Gibbs Function: G = U – TS + PV dG = dU – TdS – SdT + PdV + VdP First Law: dU = TdS – PdV dG = – SdT + VdP G(T, P)

8. Thermo & Stat Mech - Spring 2006 Class 87 Internal Energy dU = TdS – PdV U(S, V)

9. Thermo & Stat Mech - Spring 2006 Class 88 Enthalpy dH = TdS + VdP H(S, P)

10. Thermo & Stat Mech - Spring 2006 Class 89 Helmholtz Function dF = – PdV – SdT F(V, T)

11. Thermo & Stat Mech - Spring 2006 Class 810 Gibbs Function dG = – SdT + VdP G(T, P)

12. Thermo & Stat Mech - Spring 2006 Class 811 All Four dU = TdS – PdV U(S, V) dH = TdS + VdP H(S, P) dF = – PdV – SdT F(V, T) dG = – SdT + VdP G(T, P)

13. Thermo & Stat Mech - Spring 2006 Class 812 Maxwell Relations

14. Thermo & Stat Mech - Spring 2006 Class 813 Legendre Transformation If Y is a function of x, i.e. Y = Y(x), the Legendre transformation provides a means to create a new function , which is a function of D, where, The independent variable is changed from x to

15. Thermo & Stat Mech - Spring 2006 Class 814 Legendre Transformation

16. Thermo & Stat Mech - Spring 2006 Class 815 Legendre Transformation The equation of the tangent line is, Y = Dx + , where, Then,  = Y – Dx, and

17. Thermo & Stat Mech - Spring 2006 Class 816 Legendre Transformation To change more than one variable,  = Y – D 1 x 1 – D 2 x 2, etc.

18. Thermo & Stat Mech - Spring 2006 Class 817 Legendre Transformation Examples: U(S, V) Change from S to T. F = U – TS

19. Thermo & Stat Mech - Spring 2006 Class 818 Tds Equations

20. Thermo & Stat Mech - Spring 2006 Class 819 Joule-Thomson coefficient h = u+Pv dh = đq + vdp = Tds + vdp = 0 Tds = – vdP