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Thermodynamic Driving Forces: Understanding Laws and Calculations

This chapter dives into thermodynamics, covering essential concepts like thermodynamic systems—open, closed, and isolated—as well as the role of surroundings and boundaries. It presents fundamental equations related to entropy, energy, and equilibrium, emphasizing the importance of maximizing total entropy for systems in thermal equilibrium. The chapter also outlines the two laws of thermodynamics, terms such as state and process variables, and explores the applications of these principles in reversible and irreversible processes. Perfect for students and professionals seeking clear insights into thermodynamic behavior.

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Thermodynamic Driving Forces: Understanding Laws and Calculations

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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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