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Physics I Review & More Applications Prof. WAN, Xin

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Moments of Joy

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我的竺院寄语 F 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。

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

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

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

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Electrolysis 0 f H (kJ) f G (kJ) S (J/K)C P (J/K) H 2 O (l) H 2 (g) O 2 (g)

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

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

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Electrolysis U = 282 kJ P V = 4 kJ (pushing atmosphere away) T S = 49 kJ (heat) G = 237 kJ (electrical work) System At room temperature & atmospheric pressure

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Fuel Cell (Reverse Process) U = -282 kJ P V = -4 kJ T S = -49 kJ (heat) G = -237 kJ (electrical work) System At room temperature & atmospheric pressure At – electrode: At + electrode:

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Fuel Cell (Reverse Process) Maximum electrical work produced: 237 kJ Efficiency (ideal) At – electrode: At + electrode: benefit ( G) cost ( H)

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Fuel Cell (Reverse Process) Two electrons per mole of H 2 O Voltage (ideal) At – electrode: At + electrode: practically, Volt

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

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

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Introducing Free Energy F Introduce free energy F = U - TS Maxwell relation

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Van der Waals Gas F Equation of state attractive

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Van der Waals Isotherms Density fluctuation very large!

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

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

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Clausius-Clapeyron Relation F Along the phase boundary, the Gibbs free energies in the two phases must equal to each other. dT P T dP Latent heat: L = T(S g – S l ) Volume difference: V = V g – V l or

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

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A Microscopic Review F Boltzmann’s formula F 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.

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A Microscopic Review F Thermodynamic identity F Total energy is conserved. 0

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

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A Microscopic Review F Partition function F Normalized distribution

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

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App. 5: Vibration of Diatomic Molecules The allowed energies are E(n) = (n + 1/2) 1/k B T

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Specific Heat of Diatomic H 2

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

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Force toward Equilibrium F 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. F At constant temperature and volume, F tends to decrease (no particles enter or leave the system). –The total entropy (system + environment) increases. T -dU

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

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

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The End Thank you!

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