Download presentation

Presentation is loading. Please wait.

Published byAlize Cady Modified over 3 years ago

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

3
Maxwell Relations l 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 l Examples: dU = TdS – PdV dH = TdS + VdP dA = -PdV – SdT dG = VdP - SdT

4
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.

5
S(V) ( S/ V) T = ( P/ T) V dS T = [( P/ T) V ]dV S = ∫ [( P/ T) V ]dV l For Ideal Gas: P = nRT/V ( P/ T) V = nR/V S = ∫ nRdV/V = nRln(V 2 /V 1 ) const T For V 2 > V 1 S > 0

6
S(P) - ( S/ P) T = ( V/ T) P dS T = - [( V/ T) P ]dP S = - ∫ [( V/ T) P ]dP l For Ideal Gas: V = nRT/P ( V/ T) P = nR/P S = - ∫ nRdP/P = - nRln(P 2 /P 1 ) const T For P 2 > P 1 S < 0

7
U (T, V) l dU = TdS – PdV ( U/ V) T = T( S/ V) T - P From Maxwell: l 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)

8
H (T, P) l dH = TdS + VdP ( H/ P) T = T( S/ P) T +V From Maxwell: l 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)

9
“Natural” Independent Variables l U = f(S, V) l H = f(S, P) l A = f(V, T) l G = f(P, T)

10
Next Time l Gibbs-Helmholtz Equation l Fugacity

Similar presentations

Presentation is loading. Please wait....

OK

Dr Roger Bennett Rm. 23 Xtn. 8559 Lecture 6.

Dr Roger Bennett Rm. 23 Xtn. 8559 Lecture 6.

© 2018 SlidePlayer.com Inc.

All rights reserved.

Ads by Google

Ppt on history of olympics for kids Ppt on history of olympics gymnastics Ppt on bill gates leadership Download free ppt on srinivasa ramanujan Sample ppt on business plan Download ppt on teamviewer Ppt on porter's five forces model analysis Water saving tips for kids ppt on batteries Ppt on formal education will make you a living Ppt on student leadership