Thursday, November 14, 2019
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 system entropy, volume and XI’s this idea may be abbreviation (1-1)     U = U(S, V, XI)      In system of constant mass and composition, whose work can be expressed only in terms of its PV properties, there are no X’s and U is changed only by reversible 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 function 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 amount 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. Equation (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 form as equation (1.9). By comparison with equations (1.7a), and (1.8), equation (1.2) may be written as                          dU = (U/S)V dS + (M/V)S dV, form which it follows that           T = (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)T and from equation (1-4) and (1-7), (1-12)     V = (H/P)S = (G/P)T And from equation (1-6) and (1-7),
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