Lecture 8 Notes:Thermodynamics

Physics 102.002Prof. Michael Gold

September 24, 2007

September 25, 2007 physics 102.002 Lecture 8 1

All matter is made up of atoms.

Thermodynamics: Empirical lawsdescribing average properties of bulkmatter.

Atoms are very small (~0.1 nm) andtherefore bulk matter contains a veryvery large number of atoms.Avogadro’s number NA=6.02x1023

September 25, 2007 physics 102.002 Lecture 8 2

Statistical MechanicsLaws of thermodynamics can be understood (in factrigorously derived) from the average behavior ofmolecules (atoms).

Thermodynamic laws are rigorously obeyed because thetypical number of molecules is so huge that typicaldeviations from average are immeasurably small and theprobability of large deviations is infinitesimally small.

September 25, 2007 physics 102.002 Lecture 8 3

TemperatureA measure of the mean kinetic energy of moleculesper degree of freedom.

Degree of freedom is the number of ways amolecule can move.

Monatomic: f=3 displacement (vx,vy,vz)

Diatomic: f=5 displacement plus 2 rotationalmodes at moderate temperatures.

September 25, 2007 physics 102.002 Lecture 8 4

HeatA form of energy (molecular kinetic energy)that is transferred between materials as aresult of differences in temperature throughdirect (“thermal”) contact.

Heat always flows fromhot to cold.

September 25, 2007 physics 102.002 Lecture 8 5

EntropyA measure of molecular disorder:

The arrow of time: disorder of universe alwaysincreases with time.

Perpetual motion machines are impossible.

A thermodynamic limit to the efficiency of engines.

September 25, 2007 physics 102.002 Lecture 8 6

How do weknow this?

September 25, 2007 physics 102.002 Lecture 8 7

Law of definiteproportions

Whenever a given compound is formed from twoelements, the ratio of the combining masses ofthe elements is observed to be constant. Thisholds for every compound although the massratio is different for each compound.

Dalton (1807)-- Atoms of eachelement have a definite mass.

September 25, 2007 physics 102.002 Lecture 8 8

Example32g O + 12g C = CO2 carbon dioxide

16g O + 12g C = CO carbon monoxide

Ratio of oxygen in 2 compounds is 2:1

September 25, 2007 physics 102.002 Lecture 8 9

Definition of a Mole1 mole is an Avogadro’s number of things(usually molecules).

Like 1 dozen.

Empirically defined as the number of carbon atoms in

12 g of carbon.

September 25, 2007 physics 102.002 Lecture 8 10

Definition of amuThis also defines the atomic mass unit (amu).

12 amu is the mass of 1 carbon atom = mass of 1 moleof carbon / Avogadro’s number= 12g/Avogadro’snumber. Obviously a very small number.

The “12” comes from the fact that the carbon-12 atomContains 6 protons + 6 neutrons (+6 electrons ofnegligible mass). So 1amu is very nearly the mass ofa proton or neutron.

September 25, 2007 physics 102.002 Lecture 8 11

Examples1 mole of hydrogen has a mass of 1g.

the hydrogen atom has a mass of 1amu.

1 mole of oxygen has a mass of 16g. The oxygen

atom has mass of 16 amu.

September 25, 2007 physics 102.002 Lecture 8 12

DensityDensity = Mass/volume

Water density = 1g/cm3

Water is quite dense. We can measureless-dense substances relative to water

via Archimedes’ principle

September 25, 2007 physics 102.002 Lecture 8 13

Density of Ice

density = 0.92 g/cm3

Think about the implications of this fact for life!

Unusual property that solid state is lessdense than liquid state.

September 25, 2007 physics 102.002 Lecture 8 14

Archimedes

W

FBW=FB

g x (mass of object) = gx (mass of displacedwater)

September 25, 2007 physics 102.002 Lecture 8 15

PressureP = F/(area)

September 25, 2007 physics 102.002 Lecture 8 16

States of mattersolid , liquid , gas

High temperatures

plasma: ionized gas (e.g. inside fluorescentlamps, stars)

Very high temperatures: quark-gluon plasma

At very low temperatures

Super-fluid (zero viscosity fluid, liquid He-4

Super-conductor

September 25, 2007 physics 102.002 Lecture 8 17

MeasuringTemperatureMost substances expandwhen heated

September 25, 2007 physics 102.002 Lecture 8 18

Measure of Heat

1 calorie = heat required to increase thetemperature of 1g water by 1 degree C

Note: food “Calorie” = 1 kilocalorie

September 25, 2007 physics 102.002 Lecture 8 19

Ideal GasesImportant experiments with gasesleading to the ideal gas law. Idealmeans the limit of non-interactingmolecules. An excellentapproximation for many gases.

September 25, 2007 physics 102.002 Lecture 8 20

P is pressure, V is volume

n is number of moles of the gas

T is the absolute temperature (Kelvin)

R is a universal constant 8.31 J/(mole K)

Ideal Gas Law

September 25, 2007 physics 102.002 Lecture 8 21

Absolute Temperature (Kelvin scale)

September 25, 2007 physics 102.002 Lecture 8 22

Microscopic ViewA measure of the mean kinetic energy of moleculesper degree of freedom.

September 25, 2007 physics 102.002 Lecture 8 23

Why is there no hydrogen in theatmosphere?

Therefore, hydrogen is an energy storage device,not a source of energy on earth.

At atmospheric temperatures, H atoms move veryfast on average, with a significant fractionexceeding the earth’s escape velocity. Over time,the H escapes earth’s gravity.

We can produce H by separating water whichrequires energy.

September 25, 2007 physics 102.002 Lecture 8 24

Microscopic view of pressure

Atomic collisions are perfectly elastic.

How can this be?

September 25, 2007 physics 102.002 Lecture 8 25

Measuring Avogadro’sNumber

Einstein (1905) explained Brownian motion(1828) -- the random motion of small particlessuspended in liquid-- an terms of motion ofmolecules of which the liquid is composed.

R is displacement of particle of radius r in time t

September 25, 2007 physics 102.002 Lecture 8 26

Perrin’s Experiment (1908)

Devised technique to produce small resin spheres of

Uniform size of about 10-6 m (micron)

Measured NA = 6 x 1023

September 25, 2007 physics 102.002 Lecture 8 27

“Weighing” the Atom

Mass of atom =

(atomic mass units)/ Avogadro’s number

September 25, 2007 physics 102.002 Lecture 8 28

Boltzman’s Constant k