Chapter 7 Thermodynamic Driving Forces - University of ：7章热力学驱动力-大学.pptVIP

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] Review 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 - Σ μj 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 + Σ μj 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