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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

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chapter 7 thermodynamic driving forces

Chapter 7: Thermodynamic Driving Forces

“Thermodynamics is Two Laws and a Little Calculus”

i definitions
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
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
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
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
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
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
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
Two Laws of Thermodynamics
  • First Law

dU = δq + δw

dU = T dS – p dV (for closed system)

  • Second Law

dS = δq/T

more definitions1
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
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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