Outline ??

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???
??? ??????? ???????? ????????
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Outline??

• Prelude, ??
• What is heat? ?????
• Thermodynamics and times arrow. ????????
• Thermodynamics and atomic hypothesis. ????????
• Thermodynamics in the 21th century. ?????????

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References????

• ????
• Wikipedia ????
• The 2nd law, by Atkins. (????)
• Middle world, the restless heart of matter and
  life, by Mark Haw (?????)

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Prelude??
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What is thermodynamics????????
From Wikipedia, the free encyclopedia

• Thermodynamics is a physical science that studies
  the effects on material bodies, and on radiation
  in regions of space, of transfer of heat and of
  work done on or by the bodies or radiation. It
  interrelates macroscopic variables, such as
  temperature, volume and pressure, which describe
  physical properties of material bodies and
  radiation, which in this science are called
  thermodynamic systems.
• PVNRT

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What is thermodynamics? ??????? (19th century)

• Historically, thermodynamics developed out of a
  desire to increase the efficiency of early steam
  engines, particularly through the work of Nicolas
  Léonard Sadi Carnot (1824).

Scottish physicist Lord Kelvin was the first to
formulate a concise definition of thermodynamics
in 1854
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What is thermodynamics????????

• F ma
• F mg

• pV nRT
• ?Q mc?T

?? ???????????
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???????

• ????????(Ngtgt1)???

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What does thermodynamics tell us???????????

• What is heat.
• ????
• The direction of times arrow
• ?????
• More is different
• ??????

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In thermodynamics, there are 4 laws????????

• Zeroth law equilibrium and temperature
• ??????
• 1st law what is heat?
• ?????
• 2nd law times arrow
• ?????
• 3rd law low temperature limit
• ?????

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1st law what is heat????? ????
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Heat as a fluid??????
From Wikipedia The initial explanations of heat
were thoroughly confused with explanations of
combustion. In the 17th century, phlogiston (??)
was thought to be the substance of heat. In 1783
Lavoisier (???) argued that phlogiston theory was
inconsistent with his experimental results, and
proposed a 'subtle fluid' called caloric as the
substance of heat. According to this theory,
the quantity of this substance is constant
throughout the universe, and it flows from warmer
to colder bodies. Conservation of heat was a
central assumption
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Joules experiment ????? (1843)
Mgh mc?T ????????? ??????????,???????
James Joule (1818-1889)
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What is heat? ?????

• Heat is a form of energy. ??????(???)
• (now it is meaningful to say absorb heat
  or release heat. )
• Heat goes spontaneously from high T region to low
  T region.
• ??????????????????? (????)
• A definition in terms of mathematics is needed!
• ????????????
• Energy of a system is E mv2/2 V(x)
• Heat in a system is (can you say Q ?)
• Actually it is only possible to write ?Q,
  (heat is a form of energy transfer)
• ????????????(???????????)

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Heat and the 1st law of thermodynamics?????????

• Work done by conservative force
• ????? (????)
• ?W ?E, (E energy of the system)
• In the presence of friction
• ??????? (????)
• ?W ?E ? ?Q,
• (?Q heat absorbed by the system ??????)
• Clausius, 1850
• ?W ?E ? ?Q 1st law of thermodynamics
• ??????????????????????????

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The implications of 1st law???????

• ?E ?W ?Q
• Heat is a form of energy transfer.
  ???????????
• Only energy-conserving process can occur.
  ??????????????
• Heat can be used to perform work. (heat engine)
  ???????

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How does heat look like?????????

• ??
• ????????
• ????
• ????????

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2nd law thermodynamics and times arrow????
????????
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Times arrow

• Why do we get older but never younger?
• ??????????
• The answer is hidden in heat engines.
• ??????(??)?

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Heat engine??(??)

• Heat engine
• extracts heat Q1 from reservoir TH, releases heat
  Q2 to reservoir TC,
• performs work W Q1? Q2.
• ??????,?????,??????????
• Efficiency W/Q1 1 Q2/Q1
• Can eventually efficiency ? 1?
• ????????100?

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Efficiency of a heat engine?????
Nicolas Léonard Sadi Carnot (1796-1832),
mathematician and one of the pioneers of
thermodynamics.

• Efficiency W/Q1 1 Q2/Q1
• Carnot efficiency ? 1? TC/TH
• In principle there is no way to transform heat
  100 into work!

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Kelvin statement of the 2nd law of
thermodynamics??????????????
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. ?????????
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Clausius statement of the 2nd law of
thermodynamics???????????????
Rudolf Clausius (1822-1888) heat cannot of
itself pass from a colder to a hotter
body. ??????????????
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2nd law and molecular motion?????????

• ?????????????
• ?????????
• ???????

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The meaning of 2nd law???????

• Energy is conserved in all processes, but not all
  energy conserving processes can happen!
• ??????????????,?????????????????
• 100 heat ? work (process A) cannot occur,
• but 100 work ? heat (time reversal of A)
  can occur.
• 2nd law (as a part of thermodynamics) refers to
  macroscopic processes only.
• ????????????
• Some macroscopic processes are not reversible!
  (Times arrow exists.)
• ???????????? (????????)

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Microscopic reversibility????????

• F m a F F(x) a d2x/dt2
• Time reversal t ? ?t, x ? x
• v ? ?v
• F ? F, a ? a
• F m a is valid under time reversal.
• There is no times arrow in microscopic
  physics.
• ??????(??????)??????????

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Microscopic reversible, macroscopic
irreversible?????????,??????????
http//www.youtube.com/watch?vRxno7tTUI4c
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Microscopic illustration of 2nd law??????????

• http//comp.uark.edu/jgeabana/mol_dyn/KinThI.html
  
• Reverse the movie, you dont see original
  lattice
• ????,?????????
• A small change in the initial condition (due to
  precision of the computer) is amplified.
• ??????????,??????????????,??????????????????
• The initial condition (lattice) is an unlikely
  arrangement, therefore you never see it again!
• ?????????????,??????????????

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How to describe irreversibility
quantitatively???????????????
Example mixing sucrose with water ?????
Times arrow maximize number of ways to
arrange the molecules. ?????????????????
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Number of ways to arrange the
molecules???????

• Two ways to describe the physical state of a
  system.
• ??????????????
• Mechanical state (microscopic state) momentum
  and position of all particles (r1, r2, ,rN
  p1, p2, ,pN), (6N variables).
  ?? ????????????(??),??6N???
• Thermodynamic state (macroscopic state)
  E,T,V,p,N,. (much less than 6N variables)
  
  ??? ??????????????????,???
  ????6N???
• A macroscopic state corresponds to many
  microscopic states.
  W(A)
  number of microscopic states for a macroscopic
  state A(T,V,N,).
• ????????????????, W(A)gtgt1.

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Boltzmanns idea
Ludwig Eduard Boltzmann (1844-1906)
S entropy ?
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Aside what is log???????

• If x ay,
• then logax y
• If the population doubles every unit time, then
• n(t) n0 2t
• If the growth rate of a population with n
  individuals is bn,
• then n(t)n0 ebt,
• e limx?0(1x)1/x2.718..
• loge x log x

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Entropy ?
W ????????????????
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Clausius and entropy??????

• In mechanics ??
• ?V/?x F when there are only conservative forces
  
• ?V/?x lt F when there are nonconservative forces
• We define potential energy V (only depend on x).
• Clausius found (before Boltzmann) ??????,????????
• T?S ?Q for reversible processes
• T?S gt ?Q for irreversible processes
• We define entropy S (only depends on
  macroscopic state of the system).
• ??????

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S statement of 2nd law????????

• S klnW, T?S ? ?Q
• Entropy of a thermally isolated system cannot
  decreases.
• ?????????????
• Microscopically, times arrow maximize number
  of ways to arrange the molecules.
• ?? ?????????????????
• Macroscopically, times arrow in the universe
  points toward where entropy of the universe
  increases.
• ?????????????????

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Thermodynamics and the origin of the
universe?????????

• It currently seems that the ultimate reason for a
  preferred time direction is that the universe as
  a whole was in a highly ordered state at its very
  early stages, shortly after the big bang, and
  that any fluctuations in it were uncorrelated.
  The question of why this highly ordered state
  existed, and how to describe it, remains an area
  of research.

http//en.wikipedia.org/wiki/Entropy_28arrow_of_t
ime29
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?????????

• ??????
• ???????
• ?????? ????????
• ??? ??????????????

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?????????
?U ?W?Q (1st law) ?Q ? T?S
(Clausius) ???U-T?S ? ?W Under constant T, ?Q
? ?(TS), ???(U-TS) ? ?W If you leave a
constant T system alone, ?W0, ???(U-TS) ? 0 F
? U-TS (free energy ???)cannot increase in a
constant T system.
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??????
F U-TS
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????

• ?????????????????????
• ?????????

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Thermodynamics and atomic hypothesis????????
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Atomic hypothesis????

• Feynman lectures on physics, Vol 1, Ch.1
• 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.

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When you think about atomic scale??????????

• Looking for basic physical laws at small scale
  ??????
• ? quantum physics, elementary particles.
  ?????????
• Connecting macroscopic phenomena with dynamics at
  atomic scale ??????????????
• ? thermodynamics and heat. ???

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The importance of atomic hypothesis
From http//physicalworld.org/restless_universe/h
tml/ru_bolt.html 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
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What did people think about atomic hypothesis?

• Newton (1642-1727) accept it with no exp
  evidence.
• Boscovich (1711-1787) 1st one who attempted to
  construct inter-atom forces, and describing
  natural phenomena from this constuction.
• Immanuel Kant (1724-1804) atoms, if they exist
  at all, are merely centers of force and have no
  separate existence!

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What made people accept atomic hypothesis????????
????

• ????? ????
• ????? ????
• ????? ? ?????

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Robert Brown and Brownian motion???????
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.
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Brownian motion????
913nm diameter plastic spheres, taken from IUS
Physics webpage (no longer exists)
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Early theories of Brownian motion???????

• From energy of light in the microscope?
• Surface tension effect?
• (1889) temperature difference between the
  solution and environment?
• Puzzle average speed of Brownian particles V ?
  t?1/2 ?
• Why were scientists unable to explain Brownian
  motion?

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Einstein, Brownian motion, and atomic hypothesis

• The Miracle year
• Albert Einstein published 4 papers in the
  Annalen der Physik in 1905.
• Photoelectric effect
• Brownian motion
• Special theory of relativity

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Einstein's theory of Brownian motion
????????? v t-1/2 ? ???? d(t) t1/2 ????
1. ??????????????????????? 2. ??????? x x1
x2 x3 3. ???? ltxgt ltx1gt ltx2gt ltx3gt 0
????????????????????? 4. ?? ltx2gt ltx12gt
ltx22gt ltx32gt 2 ltx1x2gt 2 ltx2x3gt 2 ltx3x1gt 5.
ltx1x2gt ltx1gtltx2gt 0, ltx2x3gt 0, ltx3x1gt 0.
???????????????(????)? 6. ?ltx2gt ltx12gt ltx22gt
ltx32gt 3 ltx12gt 7. ?N? ltx2gt N ltx12gt t 8.
??????? d (ltx2gt)1/2 t1/2 , ???? t ?1/2
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From Brownian motion to Avogadro number
1. ?????????? d2 6Dt, 2. ??????????????
f ?v 3. D L2/T ?f/vM/T 4.
D? ML?/T2 E 5. ???? (i)
???????????????????????? (ii)
?????????????????? (iii) ????????D?? kT
RT/NA (iv)?????NART/D? ???T?????D,?NA Perrin
NA 71023
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Einstein relation

• Drag force f ?v ???
• Diffusion due to random walk d2 6Dt
• ???????????
• To reach equilibrium D?? kT ???
• Random collisions (random walks) are related to
  the dissipation of kinetic energy to solvent
  molecules.
• ??????????????????????????????????

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Atomic picture of thermal equilibrium
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.
http//www.unmuseum.org/einstein.htm
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Thermodynamics in the 21th century ?????????
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Motor proteins?????
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Brownian motor a nanomachine???? ??????

• Motor 2
• ATP -2
• Motor2ATP-2 ? MotorATP
• MotorATP ? Motor2 ADP- P-

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Physics of Brownian motors???????

• Symmetry
• Thermal equilibrium
• Time scale on-off time b2 gt Dt gt a2

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Rotating flagella make E. coli move
Our dream Make machines that move like them!
http//www.rowland.harvard.edu/labs/bacteria/showm
ovie.php?movfluo_cell_near
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New development in the 21th century
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Epilogue more is different?? ??????

• Heat is a form of energy (transform).
• Not all energy conserving processes occur
  (direction of time times arrow).
• 21th century we are studing the strength of
  time's arrow) .
• fundamental physical laws may change, but
  thermodynamic laws are there.

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