The pressure exerted by radiation

[PainterGuy]

TL;DR Summary

Was reading about radiation pressure and couldn't understand few points. Also, trying to look at it from historical perspective.

Hi,

I was reading about the pressure exerted by radiation and need help with few points. I'd appreciate if you could help me.

Apparently independent of Maxwell, Bartoli announced in 1876 that the Second Law of Thermodynamics required the existence of a pressure due to radiation numerically equal in amount to that derived by Maxwell. Bartoli’s reasoning holds for all forms of energy streams in space and is of more general application than Maxwell’s equations.

Source: Proceedings of the American Academy of Arts and Sciences, Volume 38, By American Academy of Arts and Sciences , 1903
You can check this capture for more context: https://imagizer.imageshack.com/img922/8909/jr4O6J.jpg

Question 1:
What are those other forms of energy in this context?

In 1876 Bartoli derived the existence of radiation pressure from thermodynamics. He argued that the radiant temperature of a body can be raised by reflecting its light from a moving mirror, and therefore it is possible to transport energy from a colder to a hotter body. To avoid this violation of the second law of thermodynamics, it is necessary that light impart a pressure to the mirror. Therefore, the radiation pressure was also called "Maxwell-Bartoli pressure".

Source: https://en.wikipedia.org/wiki/Adolfo_Bartoli

Question 2(i):
I don't understand how the temperature could be raised of a body by reflecting its own light from a mirror. Could you please help me with it?

Question 2(ii):
How would it violate the second law of thermodynamics? The second law is about entropy and I don't see what light pressure has to do with entropy in this context. Kindly help me.

 

[Delta2]

Question 2(ii): An equivalent statement of the 2nd Law of thermodynamics is that there is no way to make a process or to make a device that will transfer heat from a colder to a hotter body, unless this process or device involves doing mechanical work. If you ask me why this statement is equivalent to the statement that involves entropy, I don't know the answer sorry I am not an expert in thermodynamics, but I just know that they are equivalent.

 

[Dale]

Summary:: Was reading about radiation pressure and couldn't understand few points. Also, trying to look at it from historical perspective.

I don't understand how the temperature could be raised of a body by reflecting its own light from a mirror. Could you please help me with it?

Consider a black body, it is radiating black body radiation with a black body spectrum that has a single peak frequency which depends only on the black body’s temperature. The higher the temperature the higher the peak frequency.

Now, consider a mirror reflecting the black body radiation back onto itself. If the mirror is stationary wrt the black body then the frequency of the emitted peak is the same as the frequency of the reflected peak, and therefore the temperature is also the same. Thus the reflected light cannot increase the temperature of the black body.

But if the mirror is moving towards the object then the reflected light will be blue-shifted by normal Doppler shift. This increased frequency means that the reflected light will have an increased temperature. By being exposed to this increased temperature light, the temperature of the black body can be increased.

How would it violate the second law of thermodynamics? The second law is about entropy

Yes. The entropy of a hot object is lower than the entropy of a cold object with the same energy. So if you can increase the temperature without adding energy then you can decrease the entropy in violation of thermodynamics.

According to the second law, the entropy can be reduced if external work is done. This means that the process of moving the mirrors, which increases the temperature of the radiation, must require work. That in turn means that there must be a force and therefore a pressure from the radiation.

 

[PainterGuy]

Thank you very much for the help!

But if the mirror is moving towards the object then the reflected light will be blue-shifted by normal Doppler shift. This increased frequency means that the reflected light will have an increased temperature. By being exposed to this increased temperature light, the temperature of the black body can be increased.

In the early 19th century, the concept of the visible spectrum became more definite, as light outside the visible range was discovered and characterized by William Herschel (infrared) and Johann Wilhelm Ritter (ultraviolet), Thomas Young, Thomas Johann Seebeck, and others.[11] Young was the first to measure the wavelengths of different colors of light, in 1802.[12]

Source: https://en.wikipedia.org/wiki/Visible_spectrum#History

The discovery of infrared radiation is ascribed to William Herschel, the astronomer, in the early 19th century. Herschel published his results in 1800 before the Royal Society of London. Herschel used a prism to refract light from the sun and detected the infrared, beyond the red part of the spectrum, through an increase in the temperature recorded on a thermometer. He was surprised at the result and called them "Calorific Rays".[51][52] The term "infrared" did not appear until late 19th century.[53]

Source: https://en.wikipedia.org/wiki/Infrared#History_of_infrared_science
Also check: https://en.wikipedia.org/wiki/Electromagnetic_radiation#History_of_discovery

Doppler first proposed this effect in 1842 in his treatise "Über das farbige Licht der Doppelsterne und einiger anderer Gestirne des Himmels" (On the coloured light of the binary stars and some other stars of the heavens).[6] The hypothesis was tested for sound waves by Buys Ballot in 1845.[p 1] He confirmed that the sound's pitch was higher than the emitted frequency when the sound source approached him, and lower than the emitted frequency when the sound source receded from him. Hippolyte Fizeau discovered independently the same phenomenon on electromagnetic waves in 1848 (in France, the effect is sometimes called "effet Doppler-Fizeau" but that name was not adopted by the rest of the world as Fizeau's discovery was six years after Doppler's proposal).[p 2][7] In Britain, John Scott Russell made an experimental study of the Doppler effect (1848).[p 3]

Source: https://en.wikipedia.org/wiki/Doppler_effect#History

Side note:
As it is noted above that when infrared was discovered, they produced more heat compared to the visible light, therefore some might have concluded that infrared has more energy compared to visible light. Young was able to measure the wavelengths of visible light but I'm not able to find out who calculated the wavelengths for infrared region. Initially, they must be thinking of doppler effect of light in terms of pre-relativistic terms where its speed is also affected as result of motion thru the medium. Maxwell's theory of electromagnetic waves was well formulated by 1873 and from this it won't be wrong to conclude that it must have been known that energy of electromagnetic waves is dependent upon the wavelength by then.

Yes. The entropy of a hot object is lower than the entropy of a cold object with the same energy. So if you can increase the temperature without adding energy then you can decrease the entropy in violation of thermodynamics.

According to the second law, the entropy can be reduced if external work is done. This means that the process of moving the mirrors, which increases the temperature of the radiation, must require work. That in turn means that there must be a force and therefore a pressure from the radiation.

Entropy is sometimes referred to as a measure of the amount of "disorder" in a system. Lots of disorder = high entropy, while order = low entropy.

If 100 joules of energy is added to two concrete blocks where one block is half the size of other. The temperature of the block with half the size will raise more compared to the other block but its entropy will still be lower than that of other block. Very interesting!

 

[Dale]

Entropy is sometimes referred to as a measure of the amount of "disorder" in a system. Lots of disorder = high entropy, while order = low entropy.

While this is true, it is generally misunderstood in terms of application. I think of it in terms of spreading out. Higher entropy means the energy is more spread out.

If 100 joules of energy is added to two concrete blocks where one block is half the size of other. The temperature of the block with half the size will raise more compared to the other block but its entropy will still be lower than that of other block. Very interesting!

Yes, exactly

 

[tech99]

Maxwell's theory of electromagnetic waves was well formulated by 1873 and from this it won't be wrong to conclude that it must have been known that energy of electromagnetic waves is dependent upon the wavelength by then.

My understanding is that it is the energy of a photon which is wavelength dependent, not the energy of the wave.

 

[PainterGuy]

My understanding is that it is the energy of a photon which is wavelength dependent, not the energy of the wave.

Thank you! But at that time no one even knew photons existed. I was looking at it from historical perspective.

 

[Baluncore]

Maxwell's theory of electromagnetic waves was well formulated by 1873 and from this it won't be wrong to conclude that it must have been known that energy of electromagnetic waves is dependent upon the wavelength by then.

In 1900 Planck proposed a foundation for quantum theory.
In 1905 Einstein came up with a theoretical explanation.
The relationship between wavelength and photon energy appeared during investigation of the photoelectric effect when the energy of different wavelength photons could be measured in electron volts.

 

[PainterGuy]

Maxwell's theory of electromagnetic waves was well formulated by 1873 and from this it won't be wrong to conclude that it must have been known that energy of electromagnetic waves is dependent upon the wavelength by then.

So, is it wrong what I said above?

 

[Baluncore]

So, is it wrong what I said above?

Yes. It would be wrong to conclude, a false assumption.
It took a long time for Maxwell's math to be applied and tested in experiments by Hertz, an applied mathematician who could understand Maxwell's work.

It took a long time to understand there was a relationship between wavelength and photon energy. That did not happen until 40 years after Maxwell sorted out the math equations that described Faraday's experiments.

 

[jartsa]

My understanding is that it is the energy of a photon which is wavelength dependent, not the energy of the wave.

Energy and wavelength are frame dependent.

That is true for a photon and a wave.

Pressure energy caused by a photon in a container increases when you push the container walls inwards. And the photon becomes Doppler-shifted.

Pressure energy caused by a wave in a container increases when you push the container walls inwards. And the wave becomes Doppler-shifted.

 

[hutchphd]

Maxwell's theory of electromagnetic waves was well formulated by 1873 and from this it won't be wrong to conclude that it must have been known that energy of electromagnetic waves is dependent upon the wavelength by then.

So, is it wrong what I said above?

Yes this was not known.
But the issue of more energy coming back from a moving mirror is true without invoking photons or redshifts. Only classical physics is necessary.
Classical conservation of energy requires the reflected beam from a moving mirror to push more energy back to the emitter than is being emitted.
And so the mirror needs to be doing work hence the momentum requirement for light.

 

[PainterGuy]

Yes this was not known.

Any idea what it became known? Thanks!

 

[Baluncore]

Any idea what it became known? Thanks!

When what became known?

Max Planck, in 1899-1900.
I quote wikipedia; https://en.wikipedia.org/wiki/Max_Planck#Black-body_radiation
“The central assumption behind his new derivation, presented to the DPG on 14 December 1900, was the supposition, now known as the Planck postulate, that electromagnetic energy could be emitted only in quantized form,”

 

[PainterGuy]

Yes. It would be wrong to conclude, a false assumption.
It took a long time for Maxwell's math to be applied and tested in experiments by Hertz, an applied mathematician who could understand Maxwell's work.

It took a long time to understand there was a relationship between wavelength and photon energy. That did not happen until 40 years after Maxwell sorted out the math equations that described Faraday's experiments.

My apologies! I didn't see the post quoted above earlier.

I wasn't even thinking about photons. I was trying to say that around 1873 they presumably knew that infrared radiation carry less energy compared to visible light, and ultraviolet radiation carry more energy than visible light and infrared radiation. In other words, I think that they understood the connection between radiation energy and frequency before 1900. I'm sorry if I repeating myself.

 

[Baluncore]

In other words, I think that they understood the connection between radiation energy and frequency before 1900.

I do not think that was the case. Can you name "they".
If hotter it was assumed that there was simply more radiant flux, doing more heating.

The photoelectric effect was observed first by Heinrich Hertz in 1887, then investigated by several others, until Planck explained it in 1899-1900 with; E = h⋅υ .

Planck was reluctant to suggest quantised photons because it contradicted Maxwell's concepts, but quanta were the only way Planck could explain the photoelectric effect.

 

[vanhees71]

My understanding is that it is the energy of a photon which is wavelength dependent, not the energy of the wave.

Energy, momentum, and stress (the latter also containing "pressure" as the diagonal elements of the stress tensor) are described by the energy-momentum stress tensor of the electromagnetic field. This holds true in classical and in quantum electrodynamics. In the latter case of course the energy-momentum-stress tensor is described by a corresponding local operator as any local observable in relativistic QFT.

One should not think about photons as little massless bullets but rather as a special kind of excited states of the quantized electromagnetic fields, the socalled one-photon Fock states. One should not take the historical picture of Einstein's famous 1905 paper too literally! As all of the socalled "old quantum theory" it's not a consistent theory and is long substituted by "new quantum theory": for massive particles in non-relativistic approximation by three versions of the theory due to Born, Jordan, Heisenberg ("matrix mechanics"); Schrödinger ("wave mechanics"); Dirac ("transformation theory" or better called "representation independent formulation") all in 1925-1926. The modern description of photons as field quanta is due to Born, Jordan, and Heisenberg (mostly in fact due to Jordan) in one of the famous papers of 1926 following Heisenberg's conception of the "Helgoland paper" of 1925. The field-quantization idea was first abandoned by most contemporary physicists and then rediscovered by Dirac in 1927. The reason is that you get very far with the "semiclassical approximation" (particles, particularly electrons, quantized and the em. field described still as a classical field): You can describe the photoeffect and Compton scattering in lowest order perturbation theory as well within the semiclassical theory. The quantum theory of the radiation field is needed whenever spontaneous emission becomes important, e.g., to derive the correct Planck formula of black-body radiation.

 

[PainterGuy]

One should not think about photons as little massless bullets but rather as a special kind of excited states of the quantized electromagnetic fields

Wasn't Einstein thinking of them more like massless bullets originally? Thank you!

 

[Dale]

I wasn't even thinking about photons. I was trying to say that around 1873 they presumably knew that infrared radiation carry less energy compared to visible light, and ultraviolet radiation carry more energy than visible light and infrared radiation.

This is not true. You can have a low-power UV lamp and a high-power IR lamp. The frequency/wavelength does not determine the power of a wave. It only determines the power of individual photons. Until you get the concept of something quantized there is no frequency/wavelength dependent energy.

 

[vanhees71]

Wasn't Einstein thinking of them more like massless bullets originally? Thank you!

Yes, early on he did (1905). Even 50 years later, he said, he's still struggling with the understanding of what a photon (or more generally light) "really is"; I guess this was meant as a statement that he was not satisfied with the description by QED. Again more than 50 years later, QED is the best theory we have about light, and it's also the most succeessful theory ever, as far as agreement between theory and experiments is concerned.

 

[PainterGuy]

This is not true. You can have a low-power UV lamp and a high-power IR lamp. The frequency/wavelength does not determine the power of a wave. It only determines the power of individual photons. Until you get the concept of something quantized there is no frequency/wavelength dependent energy.

Thank you very much, everyone!

@Dale I was missing an obvious point. Thanks for helping me to understand it.

The following sources confused me in a way since I didn't read them properly. I had assumed that they understood that energy of electromagnetic waves had to do with frequency or wavelength.

 

[PainterGuy]

I'm sorry that I forgot to mention the following sources in my previous post. Someone might find these useful.

HISTORY OF ULTRAVIOLET PHOTOBIOLOGY
by Philip E. Hockberger
http://photobiology.info/Hockberger.htmlThe following is an excerpt taken from a book.

Night Vision
Exploring the Infrared Universe
by Michael Rowan-Robinson
https://assets.cambridge.org/97811070/24762/excerpt/9781107024762_excerpt.pdf

 

[anorlunda]

I had assumed that they understood that energy of electromagnetic waves had to do with frequency or wavelength.

The energy of a single photon is proportional to the frequency. However, a beam of light has a variable number of photons, so the energy of the beam is not necessarily proportional the frequency.

It is like the difference between how hard it is raining and the size of a single raindrop.