chem 125 lectures 12/02-04/02 projected material this material is for the exclusive use of chem 125...
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Chem 125 Lectures12/02-04/02
Projected material
This material is for the exclusive use of Chem 125 students at Yale and may not
be copied or distributed further.
It is not readily understood without reference to notes from the lecture.
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
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
(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