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Transformative Changes in Learning and Thermodynamic Principles

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This compilation by Prof. WAN Xin explores the evolution of education, highlighting how the integration of technology blurs the lines between classroom learning and personal exploration. It underscores the importance of critical thinking over rote memorization, fostering a new generation of thoughtful learners. Additionally, it delves into thermodynamic principles, including reversible and irreversible processes, free energy, heat exchange, and phase transitions, providing a comprehensive overview of fundamental concepts in thermodynamics.

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Transformative Changes in Learning and Thermodynamic Principles

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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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