# Physics I Review & More Applications Prof. WAN, Xin

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

Moments of Joy

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)

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

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

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

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

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

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

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:

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

Fuel Cell (Reverse Process) Two electrons per mole of H 2 O Voltage (ideal) At – electrode: At + electrode: practically, 0.6-0.9 Volt

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

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

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

Van der Waals Gas F Equation of state attractive

Van der Waals Isotherms Density fluctuation very large!

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

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

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

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

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.

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

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

A Microscopic Review F Partition function F Normalized distribution

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

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

Specific Heat of Diatomic H 2

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.

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

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

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

The End Thank you!