熱力學. 陳宣毅 中央大學物理系. 大綱. Prelude What is heat? Thermodynamics and time ’ s arrow. Thermodynamics and atomic hypothesis. Thermodynamics and 21th century science. References. The internet……(copy and paste!) Wikipedia (most of the time very reliable)
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If, in some cataclysm, all of scientific knowledge were to be destroyed, and only one sentence passed on to the next generations of creatures…… I believe it is the atomic hypothesis…… all things are made of atoms – little particles that move around in perpetual motion, attracting each other when they are a little distance apart, but repelling upon being squeezed into one another.
In physics, heat, symbolized by Q, is defined as a form of energy whose absorption raises the temperature of a body, not existing in the transition state, and abstraction of which from the same body lowers its temperature. Generally, heat is a form of energy transfer, sometimes called thermal energy, associated with the different motions of atoms, molecules and other particles that comprise matter when it is hot and when it is cold.
Heat: a form of energy or a form of energy transfer?
Heat is …… (can you find Q=……?)
Mgh = W = Q
Work can raise temperature of the system.
James Joule (1818-1889)
W = E, (E: energy of the system)
W = E Q,
(Q: heat absorbed by the system)
W = E Q 1st law of thermodynamics
(heat comes from friction, heat conduction, etc)
E = W + Q
Carnot is the name of a celebrated French family in politics and science with the following members:
Nicolas Léonard Sadi Carnot (1796-1832)
Lord Kelvin(1824-1907): a transformation whose only final result is to convert heat, extracted from a source at constant temperature, into work, is impossible.
Rudolf Clausius (1822-1888): heat cannot of itself pass from a colder to a hotter body.
100% work heat (time reversal of A) can occur
dQ/T S, S: entropy
S > 0 if T1 > T2
S = dQ/T for reversible processes only……????
Q: How can you define entropy S in this strange way???
V = F·dx for conservative forces only……
We define potential energy is this strange way!
There is no time’s arrow in microscopic physics.
Raindrop splash and displacement of soil particles.
Source: USDA Natural Resources Conservation Service.
Example: mixing sucrose with water
Time’s arrow: Maximize “number of ways” to arrange the molecules.
Two ways to describe the physical state of a system.
A macroscopic state corresponds to many microscopic states. W(A): number of microscopic states for a macroscopic state A(T,V,N,…).
(find a reversible process to go from initial state to final state)
Constant temperature expansion !
E=0 Q = W = pdV = NkT dV/V
According to Clausius, S = Q/T = Nk ln[(V+ V)/V]
W VN S = k ln[W(V+V)/W(V)] = Nk ln [(V+ V)/V]
Boltzmann's contribution was vital, but had a tragic outcome. Towards the end of the nineteenth century several puzzling facts (which eventually led to quantum theory), triggered a reaction against 'materialist' science, and some people even questioned whether atoms exist. Boltzmann, whose work was based on the concept of atoms, found himself cast as their chief defender and the debates became increasingly bitter. Always prone to bouts of depression, Boltzmann came to believe that his life's work had been rejected by the scientific community, although this was far from being true. In 1906, he committed suicide. If despair over rejection, or frustration over being unable to prove his point, were contributing factors the irony would be great indeed. Soon after Boltzmann's death, clinching evidence was found for atoms, and few would ever doubt their existence again
400x, plastic spheres, each 913 nm in diameter
Brown (1827): observed irregular movement of pollens in water under microscope.
[First observation of “Brownian motion”: S. Gray, Phil. Trans. 19, 280, (1696). ]
Major contribution of Brown: made sure non-organic particles also have Brownian motion, confirmed that Brownian motion is not a manifestation of life.
The Miracle year:
Albert Einstein published 4 papers in the Annalen der Physik in 1905.
Which topic is his PhD thesis?
Albert Einstein, 1905
即: 運動距離 d(t) ~ t1/2
2. 兩次碰撞(即走三步)後的位移 x=x1+x2+x3
3. 平均位移 <x>=<x1>+<x2>+<x3>=0 因為兩次碰撞間朝任何方向移動的機率都相同。
5. <x1x2>=<x1><x2>=0, <x2x3>=0, <x3x1>=0. 因每一步所走的方向與其他步無關(獨立事件)。
6. 故<x2>=<x12>+<x22>+<x32>=3 <x12>
7. 走N步: <x2>=N<x12>~t
8. 平均移動的距離 d=(<x2>)1/2~t1/2 , 平均速率 ~ t 1/2
Nobel Prize for physics: 1926From Brownian motion to Avogadro number
1. 花粉在水中的布朗運動: d2 = 6Dt, D:擴散係數
2. 花粉在水中的運動受水的黏滯力: f = gv, g:阻泥係數
3. [D] = L2/T; [g]=[f]/[v]=M/T
4. [Dg] = ML2/T2 = [E]
(iii) 要達成熱平衡需要Dg = kT = RT/NA
實驗:量T, g, D,得NA
Perrin: NA = 7×1023
Big ball gets kinetic energy from small balls from random collisions.
Small balls gets kinetic energy from big ball from viscous drag (turns kinetic energy of the big ball into heat).
Equilibrium: energy from big ball to small balls = energy from small balls to big ball
Equilibrium kinetic energy of the big ball = equilibrium kinetic energy of a small ball = (3/2)kT.
J = s E
Question:sas T ? as T ?
Entropy of the wire does not increases?
H. Noji, R. Yasuda, M. Yoshida, K. Kinoshita Jr, Nature, 386, 299 (1997)
Make machines that move like them!
Arrow of time : Why did the universe have such low entropy in the past, resulting in the distinction between past and future and the second law of thermodynamics?