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Modern Physics for Frommies IVThe Universe - Small to Large

Lecture 5

Fromm Institute for Lifelong Learning University of San Francisco

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Agenda•Administrative matters

•Normal Conductivity

•The Discovery of Super Conductivity

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Administrative Matters

Reduced mass: Checked, correct as is

1 2

1 2

1 2

11 1

m m

m mm m

Very Short Introductions:

Oxford University Press

https://www.oup.co.uk/vsi

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Normal ConductivityCurrent is flow of charge. Units of Coulombs (C)/sec = Amperes (A)

Analogy with the flow of water through a pipe

hP = Wgh

F

There is frictional resistance, R, to the flow.

or P

F P FRR

One might expect that the resistance decreases with the cross sectional area of the pipe and increases with the length of the pipe.

lR

A

l

A

WNote: This is not

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Current flowing through conductor with resistance R

R

V

V IROhm’s Law

lR

A

is called the resistivity (m) and is a characteristic of the material 0 01T T T

is called the temperature coefficient of resistance of the material.

l is length of conductor

A is conductor’s cross sectional area

For small T

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TT0

Ij

A

(conventional) curremt density

Electrons drift against electric field bouncing off atoms

Reach a more or less steady average speed Drift velocity vd << average random speed

vd is not the velocity of a signal, there is a “pipeline” effect.

or l

El jA E jA

Ohm’s Law

Near room temperature

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As temperature increases, the number of collisions increases, increasing the resistance to electrical flow.

Collisions generate heat. Energy id dissipated into the environment. Joule heating.

2P I R IV

As T is reduced to low levels eventually plateaus

T

Plateau dominated by scattering from impurities. Dependent on purity and thermal history

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The Road to Extremely Low Temperatures

Absolute Zero: Is there a lowest temperature?

(1740 – 1845) Kinetic Theory of Gasses

B

B

PV Nk T

NP k T

V

T (ºC)≈ -273

PressureDifferent gasses

0 K ≈ -273º CT < 0 K is meaninglessCan approach but never reach (3rd law of thermodynamics)

extrapolation

Measure the pressure of a constant volume of various gasses as a function of temperature.

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Liquifaction of Gasses: Elements and compounds that are gasses at STP

1833 Michael Faraday liquefies chlorine with water ice.

Cl2H2O crystals HOT COLD

LCl2

High pressure raises boiling point.

At STP Cl2 boils at -34 ○C

Technique also succesful for liquefying NH3, H2S, NO2, SO2, and solidifying CO2.

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1870 Louis Cailletet attempts to liquefy C2H2 . His apparatus springs a leak. Rapid release of pressure causes cooling. In 1877 he succeeds in liquefying oxygen.

At the same time Pierre Picet also succeds with oxygen by cascading Faraday’s technique

Cailletet goes on to do nitrogen and carbon monoxide

The rapid expansion effect is today known as Joule - Thomson cooling.

Hydrogen remains stubborn as does the newly discovered (1868 in solar spectrum) helium

!898 James Dewar succeeds in liquefying H2. Boiling point – 253 ○C or 20 K

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1908 H. Kammerlingh Onnes (Leiden) liquefies He at 4.2 K.

1853 - 1926

1911 Discovers superconductivity in mercury

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Low Temperature Summary

Substance and Event T (○C) T (K)

Water boils 100 373

Water freezes 0 273

SO2 boils 263

Cl2 boils 195

H2S boils 212

CO2 sublimates 195

CH4 boils 112

O2 boils 90

N2 boils 77

H2 boils 20

He boils 4.2

Absolute zero = - 273 ○C

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Now that Ommes had LHe he could measure resistivities at temperatures in the 1 K region.

Tried various materials including very pure mercury (Hg)

Hg Tc≈ 4 K Most materials

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Critical temperature, marks phase change: normal superconducting

,CT

Superconductivity is destroyed by a sufficiently high field or equivalently by a high enough current

B

Superconductivity appears in metals whose normal conductivity is not particularly high, e.g. Hg, Sn, Pb, Ga, Nb.

1931: Superconductivity found in alloys. Component elements may be non superconducting.

Some alloys will support much higher fields before going normal, e.g. NbSn.

B

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1933 Meissner effect:Magnetic fields are expelled from super conductors

Surface currents are generated which screen the interior of the superconductor.

Currents give rise to an exterior magnetic field which will act to repel the original magnet. Levitation

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