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Chapter 7: Thermodynamic Driving Forces

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

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Chapter 7: Thermodynamic Driving Forces

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  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

  5. II. Fundamental Thermodynamic Equations: Entropy • S(U, V, N1, N2, …) • dS = (δS/δU)V,NdU + (δS/δV)U,NdV + Σ(δS/δNj)V,U,Ni dNj Eqn 7.1 • dS = T-1 dU + pT-1 dV - Σμj T-1 dNj Eqn 7.5 • Note: dV, dNj, dU are differences in the degrees of freedom (DegF). p, μj, 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,NdS + (δU/δV)S,NdV + Σ(δU/δNj)V,S,Ni dNj Eqn 7.2 • dU = TdS - pdV + Σμj dNj 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 (SA, UA, TA) + Object B (with similar properties); variables = UA, UB; constant = V, N  ST(U) = SA + SB = S(UA, UB) • UT = UA + UB = constant  constraint dU = dUA + dUB = 0 or dUA = - dUB • To maximize entropy: dST= 0 = (δSA/δUA)V,NdUA + (δSB/δUB)V,NdUB • (δSA/δUA)V,N = (δSB/δUB)V,N 1/TA = 1/TB

  9. Thermal Equilibrium (2) • What does this mean? 1/TA = 1/TB  TA = TB • 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 dST = (1/TA - 1/TB)dUA

  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 = -pext dV (quasi-static process) • ΔV = 0 • Δp = 0 isobaric • ΔT = 0 isothermal • q = 0 adiabatic • Entropy • Cycles

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