Lecture-1. Governing Laws for Thermal Radiation

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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
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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
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A scene from Silence of the lambs
taken with an ordinary camera
taken with an infrared camera
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RELEVANCE OF THERMAL RADIATION
When no medium is present radiation is the
only mode of heat transfer
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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)
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SPEED, FREQUENCY and WAVELENGTH
For a medium other than vacuum
The frequency stays the same so,
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COMMON UNITS FOR WAVELENGTH
1 micrometer 10-6 m
1 nanometer 10-9 m
1 angstrom 10-10 m
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Example 1.1 (Calculate energy of photons)
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THERMAL RADIATION
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1.6 Geometrical Considerations
1.6.1 Normal to a Surface Element
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1.6.2 Solid Angle
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Example 1.2
Derive formula for calculating the length of an
arc and the circumference of a circle.
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Derive formula for calculating the area of a
sphere
How to calculate the solid angle?
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How to calculate the solid angle?
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How to calculate the solid angle?
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Now we can complete the integration since we
know how to calculate the solid angle
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1.6.3 Area and Projected Area
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1.6.4 Radiation Intensity and Irradiation
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Irradiation
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For isotropic radiation
An important integral in radiation
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1.7 Governing Laws for Thermal Radiation
1.7.1 Black Body Radiation
Real surfaces (bodies)
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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
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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
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The angular distribution of radiation intensity
emitted by a black body
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1.7.2 Plancks Radiation Law
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Plancks Radiation Law
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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
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Example 1.4
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Example 1.4
Histogram and frequency polygon of heights of 130
students
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Example 1.4
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Example 1.4
Cumulative distribution (less than the
upper class boundary)
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Example 1.4
Students smaller than 174 cm
The relative cumulative distribution
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Example 1.4
Cumulative distribution
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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
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1.7.4 Stefan-Boltzmann Law
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1.8 Blackbody Radiation in a Wavelength Interval
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1.9 Blackbody Emission into a Medium Other than
Vacuum
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Plancks function in vacuum
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1.10 Historical Note Origin of Quantum Mechanics
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The challenge was in deriving a and b
constants from the first principle
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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
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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
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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