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Review & More Applications

Physics I. Review & More Applications. Prof. WAN, Xin xinwan@zju.edu.cn http://zimp.zju.edu.cn/~xinwan/. Moments of Joy. 我的竺院寄语.

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Review & More Applications

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  1. Physics I Review & More Applications Prof. WAN, Xin xinwan@zju.edu.cn http://zimp.zju.edu.cn/~xinwan/

  2. Moments of Joy

  3. 我的竺院寄语 • 今日的大学课堂内外正在发生颠覆性的变革。知识的获得变得平庸，上课时学生就可以通过无线网络搜索直接满足跳跃性思维的需求，课后更可以自由地去探索去加强和补充课堂的教学内容。课上和课下的界限即将消除，学习和研究的差别正在缩小，教师和学生的位置也开始模糊。重要的不是学过了什么，而是学到了什么，是 从只会做功课的孩子成长为会思考的人。

  4. A Macroscopic Review • For any process • For reversible process • For irreversible process • This limits the maximum work we can extract from a certain process. (1st law)

  5. Application 1: Available Work • In a thermally isolated system at a constant T • |W| = DF is the minimum amount of work to increase the free energy of a system by DF, at a constant T. The 2nd law

  6. More Available Work • Since PDV is free at a constant P • |Wother| = DG is the minimum amount of other work (chemical, electrical, etc.) needed to increase the Gibbs free energy of a system by DG, at a constant T and a constant P. previously

  7. 0 Electrolysis

  8. Electrolysis • The amount of heat (at room temperature and atmosphere) you would get out if you burned a mole of hydrogen (inverse reaction) enthalpy

  9. Electrolysis • The maximum amount of heat that can enter the system • The minimum “other” work required to make the reaction go

  10. PDV = 4 kJ(pushing atmosphere away) DU = 282 kJ DG = 237 kJ(electrical work) TDS = 49 kJ(heat) System Electrolysis At room temperature & atmospheric pressure

  11. Fuel Cell (Reverse Process) At – electrode: At + electrode: PDV = -4 kJ At room temperature & atmospheric pressure DU = -282 kJ DG = -237 kJ(electrical work) TDS = -49 kJ(heat) System

  12. Fuel Cell (Reverse Process) At – electrode: At + electrode: Maximum electrical work produced: 237 kJ benefit (DG) Efficiency (ideal) cost (DH)

  13. Fuel Cell (Reverse Process) At – electrode: At + electrode: Two electrons per mole of H2O Voltage (ideal) practically, 0.6-0.9 Volt

  14. Geometrical Interpretation • Surface U = U(S, V) (1st law) Mixed second derivative

  15. App. 2: Thermodynamic Identities • Consider an arbitrary gas with equation of state p = p(T,V).

  16. Introducing Free Energy • Introduce free energyF = U - TS Maxwell relation

  17. Van der Waals Gas • Equation of state attractive

  18. Van der Waals Isotherms Density fluctuation very large!

  19. Application 3: Phase Boundaries carbon dioxide Supercritical fluid: It can effuse through solids like a gas, and dissolve materials like a liquid.

  20. Superfluid Helium Can Climb Walls He-II (superfluid) will creep along surfaces in order to reach an equal level.

  21. P dP T dT Clausius-Clapeyron Relation • Along the phase boundary, the Gibbs free energies in the two phases must equal to each other. Latent heat:L = T(Sg – Sl) Volume difference:DV = Vg – Vl or

  22. P dP T dT Clausius-Clapeyron Relation • Along the liquid-gas phase boundary • Along the solid-liquid boundary Why? normally for ice

  23. A Microscopic Review • Boltzmann’s formula • Suppose we are interested in one particular molecule in an isolated gas. • The total number of the microstates (with the known molecule state r & v) is related to the possible states of the rest of the molecules.

  24. A Microscopic Review • Thermodynamic identity • Total energy is conserved. 0

  25. A Microscopic Review • Thermodynamic identity • Total energy is conserved. 0 Boltzmann factor

  26. A Microscopic Review • Partition function • Normalized distribution

  27. App. 4: Maxwell Speed Distribution • For a given speed, there are many possible velocity vectors.

  28. App. 5: Vibration of Diatomic Molecules • The allowed energies are E(n) = (n + 1/2) e. 1/kBT

  29. Specific Heat of Diatomic H2

  30. One More Mystery Q'h > 0 after a cycle Q'c < 0 The total entropy of an isolated system that undergoes a change can never decrease.

  31. Force toward Equilibrium • With fixed T, V, and N, an increase in the total entropy of the universe is the same as a decrease in the (Helmholtz) free energy of the system. • At constant temperature and volume, F tends to decrease (no particles enter or leave the system). • The total entropy (system + environment) increases. -dU T

  32. App. 6: Why Different Phases? • At low T, the system tends to lower the energy, forming ordered state. • At high T, the system tends to increase the entropy, forming disordered state. tends to decrease energy entropy

  33. Phase Transition: Order vs Disorder T decreases from top panel to bottom panel

  34. The End Thank you!

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