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Chem 300 - Ch 22/#2 Today’s To Do List

Chem 300 - Ch 22/#2 Today’s To Do List. Maxwell Relations Natural Independent Variables. Maxwell Relations. dZ = N dx + M dy If an exact differential If Z(x,y) is a state function (  N/  y) x = (  M/  x) y Maxwell Relation Examples: dU = TdS – PdV dH = TdS + VdP

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Chem 300 - Ch 22/#2 Today’s To Do List

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  1. Chem 300 - Ch 22/#2 Today’s To Do List • Maxwell Relations • Natural Independent Variables

  2. Maxwell Relations • dZ = N dx + M dy • If an exact differential • If Z(x,y) is a state function • (N/y)x = (M/x)y Maxwell Relation • Examples: • dU = TdS – PdV • dH = TdS + VdP • dA = -PdV – SdT • dG = VdP - SdT

  3. Maxwell Continued • ( T/  V)S = - ( P/  S)V • ( T/  P)S = ( V/  S)P • ( P/  T)V = ( S/  V)T S(V) • ( V/  T)P = - ( S/  P)T S(P) • Use the last 2 to get values of S.

  4. S(V) • ( S/  V)T = ( P/  T)V • dST = [( P/  T)V]dV • DS = ∫[( P/  T)V]dV • For Ideal Gas: P = nRT/V • ( P/  T)V = nR/V • DS = ∫nRdV/V = nRln(V2/V1) const T • For V2 > V1DS > 0

  5. S(P) • - ( S/  P)T = ( V/  T)P • dST = - [( V/  T)P]dP • DS = -∫[( V/  T)P]dP • For Ideal Gas: V = nRT/P • ( V/  T)P = nR/P • DS = -∫nRdP/P = - nRln(P2/P1) const T • For P2 > P1DS < 0

  6. U (T, V) • dU = TdS – PdV • ( U/  V)T = T( S/  V)T - P • From Maxwell: • dA = - PdV – SdT • ( S/  V)T = ( P/  T)V subst. above. • ( U/  V)T = T ( P/  T)V – P (Internal Pressure) • For ideal gas: ( P/  T)V = [(RT/V)/  T]V = R/V • ( U/  V)T = T (R/V) – P = RT/V – P = P – P = 0 • Thus for Ideal Gas: U = f (T only)

  7. H (T, P) • dH = TdS + VdP • ( H/  P)T = T( S/  P)T+V • From Maxwell: • dG = VdP – SdT • ( S/  P)T = - ( V/  T)P subst. above. • ( H/  P)T = - T( V/  T)P + V • For ideal gas: ( V/  T)P = [(RT/P)/  T]V = R/P • ( H/  P)T = - T(R/P) + V = - RT/P – V = -V + V = 0 • Thus for Ideal Gas: H = f (T only)

  8. “Natural” Independent Variables • U = f(S, V) • H = f(S, P) • A = f(V, T) • G = f(P, T)

  9. Next Time • Gibbs-Helmholtz Equation • Fugacity

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