# Maxwell's Relations Continued…. Recap Transformed internal... Maxwells Relations Continued. Recap Transformed internal energy into new fundamental groups dU=TdS-PdV {U,S,V} dH=TdS+VdP {H,S,P} dA=-SdT-PdV {A,T,V} dG=-SdT+VdP {G,T,P}!

But how do we relate these? Started relating these through transforms How to Relate Thermodynamic properties CALCULUS! Double equivalence

Lets try it Maxwells Relations Whoop-Whup-Whip! dU =TdS- PdV Lets Test WWW dH

Td S Vd P = + =T dS P dS P dS P dH

Td S Vd P = + =V dP S dP S dP S dV

dT = dS P dP S Lets test dH =TdS+VdP

Perform WWW on the G and A dA=-SdT-PdV dG=-SdT+VdP What is nice about these? _____________ Maxwells Relations

Relates entropy to measureables Plug it in relates energies to entropy and measureables dP dT dV dT -

= = d S V dV S d S P d P S d S

dP d S dV - = =

d P T dT P dV T dT V Framework for Relations _______ is better! BECAUSE OF____________ Relations Framework

Go from difficult to easy Real (P) good, conceptuals (H) bad Conceptuals to reals Higher tier conceptuals (HTC) ____________ Lower tier conceptual __________ Reals _________ X in constants vs. dX? ___________

Relations Framework ?s 1. Is there a ____ in _____? 2. Is there a ____ in ___? 3. Is _ in ________? 4. Is there a ___? Practice Problem Lets walk through the steps/?s Isenthalps for TS diagram

Helps visualize heat transfer dT =? dS H Practice Problem Is there a HTC in the constants?

_____ What do I use? ___________ Practice Problem Is there an HTC in the dX place? ____ What do I do? ___________

Practice Problem Is there an S in the constants place? _____ What do I do ________________ Practice Problem Is there a dS?

_________ What do I do __________ Practice Problem How do we get rid of d S ?

dV P Alternative option for dS Heat Capacity (Measureable) How are they defined? How do I get from THESE to dS??? d

S How do I from ?to heat dV P Capacity?? Practice Problem dS Strategy is ________ if measureables, Else _______

Framework Revised 4. Is there a dS? _____________ Must remove S entirely _____________ Heat capacity relationship 5. EOS, properties, or measureables?

What about an EOS? Take the necessary derivatives In your example use IG Law Cp=1.5R What about properties? Plug THEM in

1 r= V 1 dV d lnV = =b dT P V dT P

- 1 dV d lnV - = =k dP T V dPT

Our Example: b dP = dT V k Summarize: Framework Steps

1. Get rid of 2. Get rid of 3. Get rid of 4. Get rid of 5. Plug in 6. Check units Side Note: How does THIS work: 1 dV

d lnV = dT P V dT P Step 0: Funky Functions: LnV, 1/V=rho, P^2, etc Funky Functions