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Maxwell’s Relations

Maxwell’s 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.

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Maxwell’s Relations

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  1. Maxwell’s Relations Continued….

  2. 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

  3. How to Relate Thermodynamic properties • CALCULUS! • Double equivalence

  4. Let’s try it

  5. Maxwell’s Relations

  6. Whoop-Whup-Whip!

  7. Let’s Test WWW

  8. Let’s test

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

  10. Maxwell’s Relations • Relates entropy to measureables • “Plug it in” relates “energies” to entropy and measureables

  11. Framework for Relations

  12. _______ is better! • BECAUSE OF____________

  13. 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? ___________

  14. Relations Framework ?’s • Is there a ____ in _____? • Is there a ____ in ___? • Is _ in ________? • Is there a ___?

  15. Practice Problem • Let’s walk through the steps/?’s • Isenthalps for TS diagram • Helps visualize heat transfer

  16. Practice Problem • Is there a HTC in the constants? • _____ • What do I use? • ___________

  17. Practice Problem • Is there an HTC in the dX place? • ____ • What do I do? • ___________

  18. Practice Problem • Is there an S in the constants place? • _____ • What do I do • ________________

  19. Practice Problem • Is there a dS? • _________ • What do I do • __________

  20. Practice Problem • How do we get rid of • Alternative option for dS

  21. Heat Capacity (Measureable) • How are they defined? • How do I get from THESE to dS??? • How do I from to heat Capacity??

  22. Practice Problem • dS – Strategy is ________ if measureables, Else _______

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

  24. What about an EOS? • Take the necessary derivatives • In your example use IG Law • Cp=1.5R

  25. What about properties? • Plug THEM in • Our Example:

  26. Summarize: Framework Steps • Get rid of • Get rid of • Get rid of • Get rid of • Plug in • Check units

  27. Side Note: • How does THIS work: • Step 0: Funky Functions: • LnV, 1/V=rho, P^2, etc…

  28. Funky Functions

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