Maxwell Relations :: essays research papers fc

My topic for the report is Thermodynamics Maxwell Relations, and in this report I will show how to derive the Maxwell Relations, as well as give several examples of how and when they are supposed to used.The change in U depend on the changes in the administration entropy, volume and XIs this idea may be abbreviation(1-1)U = U(S, V, XI)In system of constant mass and composition, whose usage can be expressed only in terms of its PV properties, there are no Xs and U is changed only by rechargeable heat and P dV work. Therefore(1-2) dU = T dS P dV.The differential of the accumulated internal energy in a fixed-composition, P dV work system is.= dH = dU + d(PV)(1-3) = dU + P dV + V dP.Substituting equation (1-2) in equation (1-3), we obtain(1-4)dH = T dS + V dP.From the defining the Helmholtz employment A we obtain( 1-5)dA = dU d(TS) = dU T dS S dT.Substituting equation (1-2) in equation (1-5)(1-6)dA = -S dT P dV. From the Gibbs Free Energy equation and equation (1.4)(1.7)dG = - S dT + V dP.We have in equations (1-2), (1-4), (1-6), and (1-7) expressed dU, dH dA, and dG in terms of P, V, T, and S. We know that thermodynamic properties have exact differentials. If a property M is a function of x and y,(1.7a)M = M(x,y)then a differential change in M, dM, is the sum of the fare that M changes in the interval dx, with y held constant, plus the amount that M changes in the interval dy, with x held constant (see figure 1.1), or(1.8)dM = (M/X)y dx + (M/Y)x dy.The terms (M/X)y and (M/Y)x are called partial derivatives of M and dM is called total differential. par (6-8) can be written(6.9)dM = B dx + C dy,where B and C represent (M/X)y and (M/Y)x respectively.Now equations (1.2), (1.4), (1.6), and (1.7) are total differentials, and have the same manikin as equation (1.9). By comparison with equations (1.7a), and (1.8), equation (1.2) may be written asdU = (U/S)V dS + (M/V)S dV,form which it follows thatT = (U/S)V and P = -(U/V)S In a like manner, from equation (1-4 ) and (1-2) we obtain(1-10)T = (H/S)P = (U/S)V ,And from equation ((1-2) and (1-6),(1-11)P = -(U/V)S = -(A/V)Tand from equation (1-4) and (1-7), (1-12) V = (H/P)S = (G/P)TAnd from equation (1-6) and (1-7),