This month our blog looks at the temperature of the Sun, and how we know this. We look at the lives and physics of two of Germany’s Nobel prize winners for physics; Wilhelm Wien and Max Planck.
Of a rather less grand nature, we are nevertheless very pleased to say that our talk on the Limousin asteroid impact of the Triassic age to the Franco-Scottish society in Dumfries on the 16th September was well received and led to some interesting questions and discussions.
Ce mois nous allons considérer la température du Soleil, et étudier la vie et le travail de deux lauréats allemands du Prix Nobel en physique; Wilhelm Wien and Max Planck.
Nous sommes heureux d'annoncer que notre conférence sur l’impact de l’asteroïde au Limousin à l'association franco-écossaise de Dumfries le 16 septembre ait bien réussi. La conférence a été suivie par une discussion animée sur le sujet.
La température du soleil
On sait depuis l’antiquité que le soleil est très chaud; même les Grecs anciens (comme Anaxagore) pensait que le Soleil était un rocher chaud. Mais la température exacte du Soleil a été decouvert il y environ 125 ans.
En janvier nous avons vu comment en 1837 Claude Pouillet a mesuré l'irrradiance solaire - et combien de chaleur per mètre carré, du Soleil on reçoit sur la Terre. Mais il fallait attendre le travail de Wilhelm Wiens pour déterminer la température effective de la photosphère
The Solar temperature
From ancient days, we have known that the Sun is hot and we have seen that the ancient Greeks, for example Anaxagoras, thought the Sun was an immensely hot rock. But just how hot has only been known for the past one hundred and twenty five years or so. In January’s blog we saw how in 1837 Claude Pouillet first measured the solar irradiance – how much heat, per square metre, from the Sun is received at the Earth. But it awaited the work of the German physicist Wilhelm Wien to determine the effective temperature of the solar photosphere.
The photosphere is the apparent surface of the Sun. As we have seen, the Sun has no firm surface; it is a huge sphere of gaseous matter which increases in density with reducing radial distance (closer to the centre of the Sun). The photosphere is the layer of the Sun where the material becomes dense enough to become opaque at visible light wavelengths.
Wien was a German physicist (1864 – 1928) who derived a semi-empirical law now called the Wien’s displacement law. (An empirical law is an equation or relationship worked out from observations rather than from theoretical understanding.)
Wien showed how the distribution of energy emitted from objects, and the peak energy levels, depended upon the temperature of the object. He showed that the colour of a hot object can be used to measure the temperature of an object. Wien’s displacement law of 1893 states:-
Wavelength(max) = b / T
Where Wavelength(max) is the wavelength at which most energy is emitted, T is the object’s temperature (in Kelvin) and b is a constant called the Wien’s displacement constant. It has value of 2.898 x 10-3 m K.
We can see this in everyday life. If we continue to heat a hot piece of metal it will become a dull red and will brighten as we heat it further. Continue to apply heat and the metal will become both brighter (because it is giving off more energy) but it will also become white.
Wien, born in Prussia into a farming family, initially struggled at school with mathematics and his early years were shaped by his intense shyness. Whilst it seemed destined he would take over the family farming interests, his parents (and particularly his mother) supported and encouraged him to gain academic skills. His ‘big-break’ happened when he attended Berlin University and started to work in the laboratories of Hermann Von Helmholtz (…see April’s blog). Wilhelm spent several years of his early career working under the auspices of Helmholtz. He held appointments at various German universities, culminating in his position of professor of physics at Munich. He developed particular interests and expertise in refraction, thermal radiation and particle physics. He received the Nobel prize for physics in 1911 for his work on electromagnetism.
Wien’s laws is a good fit for measuring temperature from high frequency emission (light and higher) but is not very accurate for measuring low frequency/high wavelength emissions. However, Wien’s work laid the basis for Max Planck (1858 – 1947) to provide the theoretical basis and understanding of thermodynamics. Planck was a true genius of theoretical physics. He was a Nobel prize winner (for quantum mechanics) in 1918, made key theoretical advances in thermodynamics, was fundamental in the origination and advancement of quantum mechanics, and extended Einstein’s special theory of relativity (the pair worked together at Berlin University from 1914). He extended Wien’s empirical work and in 1900 published the general black-body radiation energy distribution in the form of Planck’s law.
A ‘black-body’ in physics is an idealised object which, when in thermal equilibrium, (i.e. when it is in heat balance and neither increasing in temperature nor cooling down) absorbs, and radiates 100% of the energy incident (i.e. “landing-on”) the object. Or, in other words, if the surface of a star is being heated by the nuclear reactions deep inside the core, but is radiating away all the energy it is receiving; it is in equilibrium and will behave as a black-body. The black-body means that there would, for example, be no reflection or absorption of radiation; which in ‘real-life’ is never the case as ‘boundary layer effects’ also give a variance. However, it can be a very good approximation; and especially so if we are considering layers within the Sun.
Planck’s law is a little beyond the bounds of what we can realistically explained within a blog, but the interested reader is referred to our book on the Sun where details can be found. However, Planck's law can be seen graphically as below:
The graph above shows how much energy is emitted (the left hand side axis) at what wavelengths (‘colours’) for objects at various temperatures (the individual curves). Temperature here is measured in Kelvin which can be thought of as degrees centigrade but on a scale where zero Kelvin is the same as minus 273 centigrade. The red curve shows the emittance for an object at 300k, or 27 centigrade.
Although Planck’s law looks rather complicated, the distribution curves for various temperatures show us a number of key features:-
If we look at these from a Solar (Sun) perspective: The Sun’s peak of energy emission is at wavelength of around 5020 Å (Angstrom), or in SI units, ~0.5μm. From this we can deduce, from Planck’s law (or more easily, from Wien’s law) that the apparent surface temperature is around 5770K. At the peak emission of ~5000 angstroms the colour of the Sun is predominately yellow.
The Sun – shining light on the Solar system
Next month we continue our series looking at the physics of the Sun and we will look at how we know, or think we know, the temperature at the heart of the Sun.