Absorption of a photon

Question

Is it really true that focusing EM-waves of the same frequency, intensity, energetic density, on the same spot, we can rise temperature on that point indefinitely? I read there is a limit. Thanks.

-EDIT-: This solved my doubt because now I know formulas that simplify the understanding of how Power and Energy are linked in a luminous system...

Your question is unclear to me, sorry. You can stare at a book page all day, Your eyes will get tired, but they won't suffer permanent damage. This is reflected light of the same frequency, etc from an overhead lamp. — , Sep 10 '17 at 11:59
is here the answer? --->https://physics.stackexchange.com/questions/12695/heater-in-a-perfectly-insulated-box <--- — Gabriele Citossi, Sep 10 '17 at 11:59
A series of lenses concentrating on the same spot can add up to a temperature higher than the sun without violating energy conservation. The reason is because the sun is an extended body, the rays entering each lens come from a different area, although adjacent, of the sun , and there is no limit to the number of lenses that can be added except geometrical. — Gabriele Citossi, Sep 10 '17 at 12:03
Your question seems quite unclear. Please clarify your specific problem or add additional details to highlight exactly what you need. As it's currently written, it’s hard to tell exactly what you're asking. See the How to Ask page for help clarifying this question. — Wrichik Basu, Sep 10 '17 at 14:26
Possible duplicate of Is it possible to build an optical system that increases the perceived surface brightness? — Emilio Pisanty, Sep 11 '17 at 13:23
There is a property called entendue, that stops you using lenses to make a temperature hotter than the source. https://en.wikipedia.org/wiki/Etendue, fun read, https://what-if.xkcd.com/145/ — George Herold, Sep 11 '17 at 15:52
@GeorgeHerold Entendue concerns the angle...i devoured the site time ago :) — Gabriele Citossi, Sep 11 '17 at 17:11
The title of the question seems to be inconsistent with the body. It is asking about focusing em waves, not about absorption of photons. — mpv, Sep 14 '17 at 11:31
Possible duplicate of What can we deduce by the fact that mirrors cannot get a ray hotter than Sun's surface? — Mostafa, Sep 15 '17 at 12:21

score 1 · Accepted Answer · answered Sep 11 '17 at 11:48

The temperature of an object depends on the rate that heat is being added to the object and the heat that the object is losing heat to its surroundings. If you have some object at a temperature $T$ then the rate of heat loss is given by:

$$ W = kT + \sigma T^4 $$

where the first term on the right comes from Newton's law of cooling and the second term from the Stefan-Boltzmann law.

The maximum temperature of the object will be when the power radiated is equal to the power being supplied, so if the EM waves you are directing on the object have a power $P$ the maximum temperature is given by solving the equation:

$$ P = kT + \sigma T^4 $$

At very high temperatures the radiative cooling will dominate and the equation simplifies to the approximate equation:

$$ P \approx \sigma T^4 $$

or:

$$ T \approx \sqrt[4]{\frac{P}{\sigma}} $$

So, no, the temperature won't rise indefinitely. It will reach a maximum value given by the equation above.

score -1 · Answer 2 · answered Sep 10 '17 at 19:21

-1

The temperature of a body depends from the motion or vibration of the subatomic particles. Could you accelerate a subatomic particle to a greater velocity than the speed of light?
Not having any particle inside an area and shining photons of whatever intensity into this vacuum could one speak about a temperature at all?
Having a single subatomic particle in an area and fokusing intensive enough photons on this position wouldn't take place a particle creation?

It would be interesting if where are more reasons why it isn't possible to reach infinite temperature.

answered Sep 10 '17 at 19:21

HolgerFiedler

10,334

I belive it is geometrically realiable to focus more than 4Pi Stereorad of light from "one" source at a same temperature. In this case the temperature of the point will rise over the source temperature? – Gabriele Citossi Sep 11 '17 at 12:26
Your first point is completely incorrect. A particle's energy can increase without bound even with its velocity bounded by $c$. – Emilio Pisanty Sep 11 '17 at 13:25
@Emilio How this is possible? – HolgerFiedler Sep 11 '17 at 15:52
Because relativistic kinetic energy is not a quadratic function of velocity. See any introductory textbook on special relativity, or indeed the relevant sections of Wikipedia, for further details - ideally before posting more misinformation on the site. – Emilio Pisanty Sep 11 '17 at 16:50
@EmilioPisanty So the temperature of a subatomic particles does not depends from its motion (in a gas in some closed volume as well as vibrational in a rigid body)? – HolgerFiedler Sep 11 '17 at 18:24
No. Read my comments again. – Emilio Pisanty Sep 11 '17 at 19:09
@EmilioPisanty "a simplified description of fluid matter, temperature is proportional to the average kinetic energy of the random microscopic motions of the constituent microscopic particles, such as electrons, atoms, and molecules, but rigorous descriptions must include all quantum states of matter." From https://en.wikipedia.org/wiki/Temperature – HolgerFiedler Sep 11 '17 at 20:03
Your first bullet point makes the claim that the kinetic energy of a massive particle is bounded because its velocity is bounded; that is incorrect and little more than misinformation. (The rest of your claims are irrelevant to the question but they're not incorrect.) In uninterested in further discussion. – Emilio Pisanty Sep 12 '17 at 00:37

Absorption of a photon

2 Answers2