Wien’s Law and the Stefan-Boltzmann Law

Apply the Stefan–Boltzmann law to compare the luminosities of different stars.

• A radiation spectrum can give information about luminosity.
• The area under a black body radiation curve is equal to the total energy emitted per second per unit of area of the black body.
• Stefan showed that this area was proportional to the fourth power of the absolute temperature of the body.
• The total power emitted by a black body is its luminosity.
• According to the Stefan-Boltzmann law, a body of surface area A and absolute temperature T has a luminosity given by:

where, σ = 5.67x10^-8 W m^-2 K^-4

Black body radiation

• A black body is a perfect emitter. A good model for a black body is a filament light bulb: the light bulb emits in a very large region of the electromagnetic spectrum.
• The relationship between the temperature of an object and the maximum wavelength is known as Wien’s law:

State Wien’s (displacement) law and apply it to explain the connection between the colour and temperature of stars

• By analysing a star’s spectrum, we can know in what wavelength the star emits more energy.
• The Sun emits more energy at λ=500 nm.
• According to Wien’s law, the temperature at the Sun’s surface is inversely proportional to the maximum wavelength.

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State Wien’s (displacement) law and apply it to explain the connection between the colour and temperature of stars

• By analysing a star’s spectrum, we can know in what wavelength the star emits more energy.
• The Sun emits more energy at λ=500 nm.
• According to Wien’s law, the temperature at the Sun’s surface is inversely proportional to the maximum wavelength.
• So:

State Wien’s (displacement) law and apply it to explain the connection between the colour and temperature of stars

Black body radiation and Wien’s Law

Black body radiation and Wien’s Law

Star’s Colour and Temperature

Star’s Colour and Temperature

Real spectra are more complicated than this (remember emission and absorption lines?)

First attempts to classify stars used the strength of their absorption lines…

Stars were labeled “A, B, C…”

in order of increasing strength of Hydrogen lines.

Later, these categories were reordered according to temperature/color leading to OBAFGKM(LT)! …

You do not need to know this, it is just interesting how things evolved.

Eventually, the connection was made between the observable and the theory.

Observable:

• Strength of Hydrogen Absorption Lines
• Blackbody Curve (Color)

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Theoretical:

• Using observable features to determine things we can’t measure:

Temperature and Luminosity

Describe the overall classification system of spectral classes.

“If a picture is worth a 1000 words, a spectrum is worth 1000 pictures.”

What colour would these be?