热力学与统计物理 金晓峰 复旦大学物理系 2005-3-16 2018/11/28.

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1 热力学与统计物理 金晓峰 复旦大学物理系 2018/11/28

2 Carnot’s ideas Q W

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4 Carnot’s Cycle

5 Carnot’s theorem “All reversible engines operating between the same two constant temperatures TH and TL have the same efficiency. Any irreversible engine operating between the same two fixed temperatures will have an efficiency less than this.”

6 Clapeyron’s Graph

7 Clausius’ Idea

8 Clausius statement Not possible

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10 Clausius’ ideas 热力学第一定律 Q = dU + W = dU + pdV

11 dU=Q+W = Q - pdV

12 Clausius’ deduction (1865)
e= W/ QH = 1-QL/QH =1-TL/TH

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16 Clausius’ Statments “The energy of the universe is a constant.
The entropy of the universe approaches a maxium.”

17 热力学第二定律 dS  0 对孤立系统： （U, V 固定） S = Smax 达到平衡态的条件： 对非孤立系统 ？

18 Hamilton’s Principle (1834)
Fermat’s Principle (1662) “From the principle, so common and so well-established, that Nature always acts in the shortest ways.” Hamilton’s Principle (1834) If a body is at a point x1 at a time t1, and at a point x2 at time t2, the motion occurs so as to minimize a quantity called the action.

19 热力学基本方程 U(S,V) -热力学势函数 dU=dQ - PdV dQ  TdS dU  TdS - PdV
dU  0, 或 U = Umin 在S,V固定时： U(S,V) -热力学势函数

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21 求作为N,T,V函数的： 理想气体的熵 dU = TdS - PdV

22 H(S,P) -热力学势函数 dU  TdS - PdV 焓 dH  0, 或 H = Hmin
dU + d(PV) TdS – PdV +PdV +VdP d(U + PV) TdS +VdP 焓 dH TdS +VdP H = U +PV dH  0, 或 H = Hmin 在S,P固定时： H(S,P) -热力学势函数

23 F(T,V) -热力学势函数 dU  TdS - PdV dF  0, 或 F = Fmin
dU - d(TS) TdS – PdV -TdS - SdT d(U - TS) -SdT - PdV dF  -SdT - PdV F = U - TS dF  0, 或 F = Fmin 在T,V固定时： F(T,V) -热力学势函数

24 G(T,P) -热力学势函数 dU  TdS - PdV dG  0, 或 G = Gmin
dU + d(PV) - d(TS) TdS – PdV +PdV +VdP -TdS - SdT d(U + PV- TS) -SdT + VdP dG  -SdT + VdP G = U + PV- TS dG  0, 或 G = Gmin 在T,P固定时： G(T,P) -热力学势函数

25 U(S,V) H(S,P) F(T,V) G(T,P) 热力学特征函数

26 Good Physicists Have Studied Under Very Fine Teachers
dU=TdS-PdV G P H S U V F T dH=TdS+VdP 　　　 dF=-SdT -PdV dG=-SdT+VdP Good Physicists Have Studied Under Very Fine Teachers

27 TdS 是热学效应，- PdV是力学效应 对磁性体系可以有: dU=TdS+HdM 对电学体系可以有: dU=TdS+EdP 粒子数还可以变化，只要加上一项， 是化学势

28 1911 K. Onnes Superconductivity in Hg

29 History of Superconductivity
K. Onnes Superconductivity in Hg Year of Discovery Transition Temperature (K) MEISSNER EFFECT: Perfect diamagnetism Meissner effect Isotope effect Tc~M-a (a~1/2) Tunneling experiments RESISTANCELESS CONDUCTION Temperature Resistivity Metal Superconductors Tc BCS Theory BCS Theory

30 History of Superconductivity
Year of Discovery Transition Temperature (K) BCS Theory C60 MgB2 Hg-Ba-Ca-Cu-O Tl-Ba-Ca-Cu-O Bi-Sr-Ca-Cu-O Y-Ba-Cu-O La-Ba-Cu-O Hg-Ba-Ca-Cu-O (pressure) HTSC: New mechanism? Conventional SC: Phonons mediated superconductivity

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34 * 对 (I) 型超导体 在T不变的情况下，对　式，积分 * 这样 或

35 定义 而 在0<H<Hc时 比正常态能量更低 因为 所以 H = 0 而且 正常态比超导态能量高 又因为

36 在T=Tc时，连续 T<Tc时，不连续 所以 比热 或 T 在 H＝0处, Hc=0， 所以

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