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Lecture-1. Governing Laws for Thermal Radiation

Contents of the lecture

1.1 Heat Transfer Mechanisms

1.2 Electromagnetic Radiation

1.6 Geometrical Considerations

1.7 Governing Laws for Thermal Radiation

1.8 Blackbody Radiation in a Wavelength Interval

1.10 Historical Note Origin of Quantum Mechanics

1.11 Blackbody Emission into a Medium Other than

Vacuum

1.12 Summary

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The convention (in this lecture series) is

Radiation which is given off by a body because of

its temperature is called thermal radiation

A body of a temperature larger than 0 K emits

thermal radiation

A scene from Silence of the lambs

taken with an ordinary camera

taken with an infrared camera

RELEVANCE OF THERMAL RADIATION

When no medium is present radiation is the

only mode of heat transfer

ELECTROMAGNETIC WAVES

Classical theory

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SPEED, FREQUENCY and WAVELENGTH

For any wave

Determined by the source

Determined by the medium

For electromagnetic waves

c3108 m/s ( in vacuum)

SPEED, FREQUENCY and WAVELENGTH

For a medium other than vacuum

The frequency stays the same so,

COMMON UNITS FOR WAVELENGTH

1 micrometer 10-6 m

1 nanometer 10-9 m

1 angstrom 10-10 m

Example 1.1 (Calculate energy of photons)

THERMAL RADIATION

1.6 Geometrical Considerations

1.6.1 Normal to a Surface Element

1.6.2 Solid Angle

Example 1.2

Derive formula for calculating the length of an

arc and the circumference of a circle.

Derive formula for calculating the area of a

sphere

How to calculate the solid angle?

How to calculate the solid angle?

How to calculate the solid angle?

Now we can complete the integration since we

know how to calculate the solid angle

1.6.3 Area and Projected Area

1.6.4 Radiation Intensity and Irradiation

Irradiation

For isotropic radiation

An important integral in radiation

1.7 Governing Laws for Thermal Radiation

1.7.1 Black Body Radiation

Real surfaces (bodies)

BLACK BODY RADIATION

Definition of a black body

A black body is defined as an ideal body that

all incident radiation pass into it and

internally absorbs all the incident radiation.

This is true for radiation of all wavelengths and

for all angles of incidence

BLACK BODY RADIATION

Properties

Black body is a perfect emitter

In a black body enclosure radiation is isotropic

Black body is a perfect emitter in each direction

Black body is a perfect emitter at any wavelength

Total radiation of a black body into vacuum is a

function of temperature only

The angular distribution of radiation intensity

emitted by a black body

1.7.2 Plancks Radiation Law

Plancks Radiation Law

Plancks Radiation Law

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See Example 1.4 of the lecture notes to understand

the meaning of

Frequency distribution

Cumulative frequency distribution

Relative cumulative frequency distribution

Example 1.4

Example 1.4

Histogram and frequency polygon of heights of 130

students

Example 1.4

Example 1.4

Cumulative distribution (less than the

upper class boundary)

Example 1.4

Students smaller than 174 cm

The relative cumulative distribution

Example 1.4

Cumulative distribution

1.7.3 Wiens Displacement Law

We are looking for a wavelength that maximizes

the Plancks function for a given temperature

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Wiens Law

1.7.4 Stefan-Boltzmann Law

1.8 Blackbody Radiation in a Wavelength Interval

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1.9 Blackbody Emission into a Medium Other than

Vacuum

Plancks function in vacuum

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1.10 Historical Note Origin of Quantum Mechanics

The challenge was in deriving a and b

constants from the first principle

Ten years later Planck wrote My futile

attempts to fit the elementary quantum of action

(h) somehow into the classical theory continued

for a number of years, and they cost me a great

deal of efforts

In 1905 Albert Einstein made an assumption the

energy of a light was concentrated into localized

bundles later called photons

Planck, the originator of the h constant, did not

accept at once Einsteins photons. In 1913 Planck

wrote about Einstein that he sometimes have

missed the target in his speculations, as for

example in his theory of light quanta, cannot

really be held against him

In 1918 Planck received a Nobel prize for his

discovery of energy quanta

In 1921 Einstein received his Nobel prize for

his service to theoretical physics and specially

for discovery of the law of photoelectric effect

1.12 Summary

Students should understand

The concepts of radiation intensity and emissive

power

The radiation laws for black-body radiation

Plancks law

Wiens law

Stefan-Boltzmann law