Chapter 7: Thermodynamic Driving ForcesThermodynamics is Two Laws and a Little Calculus

I. DefinitionsThermodynamic system - what we studyOpen: can exchange U, V, nClosed: can exchange U, V, but not nIsolated: cannot exchange U, V, nSurroundings - everything elseBoundariesSemipermeable: allows some atoms to passAdiabatic: allows no heat to passPhase: homogeneous; uniform in p, T, [A]

More DefinitionsProperty: measurable of a systemExtensive = function of n, N, VU, S, H, GIntensive function of n, NT, P, , [A]

Review

II. Fundamental Thermodynamic Equations: EntropyS(U, V, N1, N2, )dS = (S/U)V,NdU + (S/V)U,NdV + (S/Nj)V,U,Ni dNjEqn 7.1dS = T-1 dU + pT-1 dV - j T-1 dNj Eqn 7.5Note: dV, dNj, dU are differences in the degrees of freedom (DegF). p, j, T are the driving forces. As driving forces (DF) become more uniform, d(DegF) 0.

Fundamental Thermodynamic Equations: EnergyU(S, V, N)dU = (U/S)V,NdS + (U/V)S,NdV + (U/Nj)V,S,Ni dNjEqn 7.2dU = TdS - pdV + j dNj Eqn 7.4Note: (U/S)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 = 0Identify system, variables (DegF), constantsIdentify constraints, relationshipsMaximize total entropyApply constraintCombine 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 = (SA/UA)V,NdUA + (SB/UB)V,NdUB (SA/UA)V,N = (SB/UB)V,N 1/TA = 1/TB

Thermal Equilibrium (2)What does this mean?1/TA = 1/TB TA = TBIn 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 ThermodynamicsFirst Law dU = q + wdU = T dS p dV (for closed system)Second LawdS = q/T

More DefinitionsState 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 EquationsReversible and IrreversibleWork w = -pext dV (quasi-static process)V = 0p = 0isobaricT = 0isothermalq = 0adiabaticEntropyCycles