1. Chapter 7: Thermodynamic Driving Forces “Thermodynamics is Two Laws and a Little Calculus”

2. I. Definitions Thermodynamic system - what we study –Open: can exchange U, V, n –Closed: can exchange U, V, but not n –Isolated: cannot exchange U, V, n Surroundings - everything else Boundaries –Semipermeable: allows some atoms to pass –Adiabatic: allows no heat to pass Phase: homogeneous; uniform in p, T, [A]

3. More Definitions Property: measurable of a system –Extensive = function of n, N, V U, S, H, G –Intensive ≠ function of n, N T, P, ρ, [A]

4. Review Degree of Freedom Observation (  max W) Driving Force Ex. 2.2 pressure VAs V increases, gas expands. p Ex 2.3 diffusion particle exch α N j As {N j } increases, gases mix and particle distrib  more uniform Chem potential, μ j Ex. 3.4UHeat flows until T is uniform T

5. II. Fundamental Thermodynamic Equations: Entropy S(U, V, N 1, N 2, …) dS = (δS/δU) V,N dU + (δS/δV) U,N dV + Σ(δS/δN j ) V,U,Ni dN j Eqn 7.1 dS = T -1 dU + pT -1 dV - Σ μ j T -1 dN j Eqn 7.5 Note: dV, dN j, dU are differences in the degrees of freedom (DegF). p, μ j, T are the driving forces. As driving forces (DF) become more uniform, d(DegF)  0.

6. Fundamental Thermodynamic Equations: Energy U(S, V, N) dU = (δU/δS) V,N dS + (δU/δV) S,N dV + Σ(δU/δN j ) V,S,Ni dN j Eqn 7.2 dU = TdS - pdV + Σ μ j dN j Eqn 7.4 Note: (δU/δS) V,N = T means that the increase in energy per increase in entropy is positive; as S increases, so does U and in proportion to T.

7. III. Equilibrium: dS = 0 Identify system, variables (DegF), constants Identify constraints, relationships Maximize total entropy Apply constraint Combine and rearrange to find requirement for equilibrium

8. Thermal Equilibrium (Ex. 7.2) System = isolated = Object A (S A, U A, T A ) + Object B (with similar properties); variables = U A, U B ; constant = V, N  S T (U) = S A + S B = S(U A, U B ) U T = U A + U B = constant  constraint dU = dU A + dU B = 0 or dU A = - dU B To maximize entropy: dS T = 0 = (δS A /δU A ) V,N dU A + (δS B /δU B ) V,N dU B (δS A /δU A ) V,N = (δS B /δU B ) V,N  1/T A = 1/T B

9. Thermal Equilibrium (2) What does this mean?1/T A = 1/T B  T A = T B In order to maximize entropy, energy or heat will transfer until the temperatures are equal. Will heat flow from hot to cold or vice versa? Check dS T = (1/T A - 1/T B )dU A

10. Mechanical Equilibrium (Ex. 7.3) Complete

11. Chemical Equilibrium (Ex. 7.5) Complete

12. Two Laws of Thermodynamics First Law dU = δq + δw dU = T dS – p dV (for closed system) Second Law dS = δq/T

13. More Definitions State variables (state functions) Process variables(path functions) Quasi-static process: such that properties ≠ f(time, process speed) Reversible process: special case of quasi- static such that can be reversed with no entropy change (ideal case) Thermodynamic cycle: initial = final state

14. IV. Applications of Fundamental Thermodynamic Equations Reversible and Irreversible Work δw = -p ext dV (quasi-static process) –ΔV = 0 –Δp = 0isobaric –ΔT = 0isothermal –q = 0adiabatic Entropy Cycles