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

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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)-285.83-237.1369.9175.29 H 2 (g)00130.6828.82 O 2 (g)00205.1429.38

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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, 0.6-0.9 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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Aka the Law of conservation of energy, Gibbs in 1873 stated energy cannot be created or destroyed, only transferred by any process The net change in energy.

Aka the Law of conservation of energy, Gibbs in 1873 stated energy cannot be created or destroyed, only transferred by any process The net change in energy.

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