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Chapter 7: Thermodynamic Driving ForcesPowerPoint Presentation

Chapter 7: Thermodynamic Driving Forces

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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]

- Extensive = function of n, N, V

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

Mechanical Equilibrium (Ex. 7.3)

- Complete

Chemical Equilibrium (Ex. 7.5)

- Complete

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

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