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Chapter 7: Thermodynamic Driving Forces

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# Chapter 7: Thermodynamic Driving Forces - PowerPoint PPT Presentation

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

“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
• Semipermeable: allows some atoms to pass
• Adiabatic: allows no heat to pass
• Phase: homogeneous; uniform in p, T, [A]
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]
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.
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.
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
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
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
Two Laws of Thermodynamics
• First Law

dU = δq + δw

dU = T dS – p dV (for closed system)

• Second Law

dS = δq/T

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
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