Interactive Astronomy

Wien's Law and Stefan-Boltzmannn Law for a Blackbody

Life Cycles of Stars | Diffuse Nebula | Main-Sequence Stars | Red Giants after Main-Sequence | Death of a Low Mass Star | Death of a High-Mass Star | Star Families | Magnitude Scale | Measuring Stellar Distances | Classification of stars | Wien's Law and Stefan-Boltzmannn Law for a Blackbody | Stellar Spectra

Wien's Law for a Blackbody

Wilhem Wien, a German physicist, derived this law for a blackbody, which stars in essence, are (A blackbody is a perfect object that does not reflect any light and absorbs all radiation). This law can be used to calculate the surface temperature of a star if the peak intensity wavelength is known and it is not necessary to know other details like the distance of the star from Earth to compute the answer.

 

 

Where is the wavelength of maximum emission of the object in metres and T is the temperature of the object in Kelvins.

 

Worked Example:

  • A man wants to find out the colour of a certain star. Given that the star temperature is 12 000 K, find its colour.

 

Use the formula

 

 

 

 

Therefore, the star’s colour is blue-white.

 

Stefan-Boltzmann Law for a Blackbody

This equation was derived by 2 Austrian physicists- Josef Stefan and Ludwig Boltzmann.

 

 

Where F is the energy flux, the amount of energy emitted from each square meter of an object’s surface in a second (total energy of the sun emitted in a second divided by the surface area).(sigma) is a constant of . By the way, Wm to the power of -2 stands for watts per metre square. Finally, T is the object’s temperature in Kelvins.

 

Worked Example:

  • Find the surface temperature of the Sun if its average solar energy flux arriving at Earth has been determined to be 1370 W m -2, also give that the radius of the sun is 6.96 X 10 to the power of 8 metres.

Our first step is to find the value of F, the energy flux:

 

 

 

 

 

Next, we substitute this into the equation

 

 

 

 

Therefore, the surface temperature of the sun is 5800 K.

 

Life Cycles of Stars | Diffuse Nebula | Main-Sequence Stars | Red Giants after Main-Sequence | Death of a Low Mass Star | Death of a High-Mass Star | Star Families | Magnitude Scale | Measuring Stellar Distances | Classification of stars | Wien's Law and Stefan-Boltzmannn Law for a Blackbody | Stellar Spectra

 

 

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