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