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

Carnot’s ideas Q W

Carnot’s Cycle

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.”

Clapeyron’s Graph

Clausius’ Idea

Clausius statement Not possible

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

dU=Q+W = Q - pdV

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

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

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 ？

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.

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

求作为N,T,V函数的： 理想气体的熵 dU = TdS - PdV

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

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

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

U(S,V) H(S,P) F(T,V) G(T,P) 热力学特征函数

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

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

1911 K. Onnes Superconductivity in Hg

History of Superconductivity 1911 K. Onnes Superconductivity in Hg Year of Discovery Transition Temperature (K) MEISSNER EFFECT: Perfect diamagnetism 1933 Meissner effect 1950 Isotope effect Tc~M-a (a~1/2) 1962 Tunneling experiments RESISTANCELESS CONDUCTION Temperature Resistivity Metal Superconductors Tc 1957 BCS Theory BCS Theory

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

* 对 (I) 型超导体 在T不变的情况下，对　式，积分 * 这样 或

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

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