1
!......
621
32
,
nyyyyea
ean
y
RTV Am
+++==
=Π−
Perhaps the most important power series on the Planet!
Constantly used in a process called LINEARIZATION when y is small compared to 1, e.g., if y = - 0.02
yea y +≈= 1
361 Lec27 Mon 19oct15
More Osmotic Pressure: Π = osmotic pressure = applied pressure at equilibrium Vm,A = partial molar volume of SOLVENT =L/mol if R = 0.083145 L bar K-1 mol-1 and Π in bars and a = activity = γAXA.
this is known as “linearization”
exponential power series
Fact:
2
3
4
5
6
361 Lec28 Mon 20oct14
NaDNA= Sodium salt of DNA which is a very poly-protic acid.
161800618.02
04.001.1.02
4
001.01.0
01.01.0
1.01.0
1.0
2
2
2
.-acbbx
xx
xxx
x
or
:equation quadratic
=+±−
=−±−
=
=−+
=+
=+
7
8
energy/distance =
energy/volume = energy/area =
force
pressure surface tension
Surface Tension
9
Printed in book, The Second Law by Henry Bent
10
http://www.musicofnature.org/home/american_toad_dream/
Henry Bent In human thermodynamics education, Henry Albert Bent (c.1927-) was is an American physical chemist noted for his 1965 book The Second Law, for his 1971 article “Haste Makes Waste: Pollution and Entropy”, in which he attempts at a connection between the maintenance of the environment and entropy, and for his thermodynamics workshops, where he attempted to educate students on how to live ethically according to the laws of thermodynamics. [1] Specifically, instead of a national energy policy, Bent states: "What we need is a personal entropy ethic."
11
Chapters 2-4,6,7: Thermodynamics (equilibrium states)
All about what is possible or not (never whether or how how fast)
Chapters 8-10: Study rate at which physical and chemical processes that are NOT AT EQILIBRIUM proceed to equilibrium
Chapter 9: Kinetics: rates of chemical reactions Chapter 8: About processes that depend on how fast molecules move: Diffusion Sedimentation Electrophoresis first we examine velocities of molecules
12
Calculate the average force a molecule makes on the wall.
13
Boltzmann Distribution
RT)( ΔU−∆−−−
−
−
==== egge
gge
gg
e
egg
PP Tk
UTkUU
TkU
TkU
BB
B
B
1
2)(
1
2)(
1
2
1
2
1
212
1
2
about the probability to find a molecule in to different energy levels, 1 and 2 or, the ratio of the probabilities, P2 /P1 = N2/N1 = ratio of numbers of molecules at equilibrium Recall Gibbs, Boltzmann said, independently in ~1880
where, g2/g1 is the ratio of number of microstates available in the two states. i.e., same as we have called W2/W1, where S = kBlnW also given by Boltzmann. g = W = “degeneracy” of the state.
Units ????
i.e., a histogram
14
15
Maxwell-Boltzmann Speed Distribution
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