Chem 125 Lectures12/02-04/02

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JosiahWillardGibbs

(1839-1904)

~1855

Gibbs/Nernst

Gibbs 1902

Mechanical Theory of Heat

Rudolph Clausius(1822-1888)

“Thermo dynamics”

“heat consists in a motion of the ultimate particles of bodies and is a measure of the vis viva of this motion.”

(1852)

particles

J. Willard Gibbs (1889)

“Clausius was concerned with the mean values of various quantities which vary enormously in the smallest time or space which we can appreciate.”

J. Willard Gibbs (1889)

“Maxwell occupied himself with the relative frequency of the various values which these quantities have.

In this he was followed by Boltzmann.”

J. Willard Gibbs (1889)

“In reading Clausius, we seem to be reading mechanics; in reading Maxwell, and in much of Boltzmann’s most valuable work, we seem rather to be reading in the theory of probabilities.”

James Clerk Maxwell

(1831-1879)

Distributionof Velocities

On the Motions and Collisions of perfectly elastic Spheres (1859)

f(vx)

probability ofx-velocity between

vx and vx + d vx

vx

vz

vy

v

v2 = vx2 + vy

2 + vz2

Assume vx , vy , vz are independent

g(v2) = g(vx2 + vy

2 + vz2) = f(vx) f(vy) f(vz)

ProductSum

g(vx2 + vy

2 + vz2) = c3 e-a (vx

2 + vx2 + vx

2)

f(vx) = c e-a vx2

f(v) = C v2 e-a v2

vx

vz

vy

v

f(v) = C v2 e-a v2

0.00

0

v

f(v)

1D2D

3D

MaxwellVelocity

Distribution

Got to here onDecember 2.

Remaining slidesfor December 4.

On the Relationship between the Second Law of Thermodynamics andProbability Calculationregarding the laws ofThermal Equilibrium

(1877)

S = k ln WLudwig Boltzmann

1844 - 1906

Confirmed Maxwellby considering the

implications of random distribution of energy.

Generalized to includenon-translational energy:

VibrationRotation

etc.

Random Distribution of 3 “Bits” of Energy among 4 “Containers”

How many“complexions”

have N bitsin the firstcontainer?

3

N

#

3

1

2

Random Distribution of 3 “Bits” of Energy among 4 “Containers”

How many“complexions”

have N bitsin the firstcontainer?

6

N

#

123

31

How many“complexions”

have N bitsin the firstcontainer?

0

6

N

#

123

31

Random Distribution of 3 “Bits” of Energy among 4 “Containers”

10

0

6

N

#

123

31 10

30 bits of energyin 20 molecules

3 bits of energyin 4 “molecules”

30 in 20

(N)

E

(E)

e-E/kT

Boltzmann showed Exponential limitfor lots of infinitesimal energy bits

Eave = 1/2 kT

If all “complexions” for a given Etotal are equally likely, shifting energy to any one degree of freedom of any one molecule is disfavored. By reducing the energy available elsewhere, this reduces the number of relevant complexions.

Boltzmann (1898)Lectures on Gas Theory

“I am conscious of being only an individual struggling weakly against the stream of time. But it still remains in my power to contribute in such a way that when the theory of gases is again revived, not too much will have to be rediscovered.”

Max Planck1858-1947

On the Theory of theLaw of Energy Distribution

in the Normal Spectrum(December 14, 1900)

“I had always regarded the search for the absolute as

the loftiest goal of all scientific activity”

2nd Law - Irreversibility

Max Planck1858-1947

According toMaxwell’s EM Theory

light emissionis proportional to:

Energy

2

On the Theory of theLaw of Energy Distribution

in the Normal Spectrum(December 14, 1900)

Ferdinand Kurlbaum (Berlin PTR, 1898)

“Black Body” radiation at 100°C is0.0731 watts/cm2 greater than at 0°C.

steamsteamicewater

Otto Lummer & Ernst Pringsheim

(PTR, Feb.1900)

max T = 2940 m K

max T = Const

Wilhelm Wien(PTR, 1893)

1.782 mWien

(PTR, 1896)

Equations

Planck(Oct. 19, 1900)

Wien(PTR, 1896)

Lummer &Pringsheim(PTR, Feb. 1900)

Thiesen(PTR, Feb. 1900)

“simple form…more likely to indicate the possibility of a general significance”

Why are high frequencyoscillators underpopulated?

?

"We treat E however - and this is the most significant point in the whole calculation - as composed of specific number of identical finite parts and make use for that purpose of the constant of nature h = 6.55 x 10-27 [erg x sec]. This constant multiplied by the common frequency of the oscillators [within

a given family] gives the energy element in ergs.”

Planck’s “Desperation” Hypothesis(Dec. 14, 1900)

Planck’s Hypothesis(Dec. 14, 1900)

Forced to choose between putting lots of energy into a degree of freedom, or none at all, statistics will choose none at all - until the temperature becomes high enough that localizing so large an amount of energy is not very unlikely.

Planck’s “Desperation” Hypothesis(Dec. 14, 1900)

*(h, when is large)

*

k and h Planck EmpiricalE()

Planck TheoreticalE()

Lummer and Pringsheim’s maxT = 2940 m K

gave h/k

Kurlbaum's 0.0731 watts/cm2 differencein radiant heat between 100°C and 0°C

gave k4/h3

Gave h within 1% , k within 2.5%

(Avogadro-Lohschmidt ; Faraday ; electron charge)

A critical comparisonof the two processes would

be of interest,

Lord Rayleigh (1905)

but not having succeededin following Planck’s reasoning,

I am unable to undertake it.

to

Wilhelm Wien

1911 Nobel Prize in Physicsfor work on

Black-Body Radiation

for his Displacement Law& his Spectral Distribution Law

(~valid at short wavelengths)

“The problem now became to bridge the gap between these two laws [Wien & Rayleigh]… It was Planck who solved this problem; as far as we are aware, his formula provides the long sought-after connecting link…” (Nobel Presentation Address)

as far as we are aware

March 1905Generalization that light energy

is intrinsically quantized(not just when it enters or

leaves a molecular oscillator)

Albert Einstein (age 26)

April 1906

May 1905 Theory of Brownian Motion

June 1905 Special Relativity - SpaceTime

Sept. 1905 E = mc2

Experte III. Klasse Experte II. Klasse

Max Planck(1858-1947)

Nobel Prize 1918

Succeeded (1928) by Erwin Schrödinger

PresidentKaiser Wilhelm Society1930-1937

Brought Einsteinto Berlin (1914)

“Reluctant Revolutionary”

; 1945-1946