# How does light carry heat

Discussion in 'Physics & Math' started by Magical Realist, Mar 3, 2017.

1. ### DaveC426913Valued Senior Member

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No.

Einstein won the Nobel prize for the photoelectric effect - the ability for light to give a physical kick to matter.

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3. ### Magical RealistValued Senior Member

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Force = mass x acceleration?

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5. ### DaveC426913Valued Senior Member

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While that is one formula, that is not an exhaustive definition of force.

Here is another, relating frequency of a photon to its maximum kinetic energy:
Kmax = h(ƒ − ƒ0)

Last edited: Mar 4, 2017
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7. ### Q-reeusValued Senior Member

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You've had some answers already on that one. I had assumed that at an early stage in any radar techie course, a chart showing the full EM frequency/wavelength spectrum - ELF radio up to gamma rays - would have been mandatory. Can't recall that happening? No intro to Maxwell's equations?

8. ### exchemistValued Senior Member

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I wonder if it may be helpful here to mention that an electric charge can give a "kick' to another charge, or a magnet can give a "kick" to a steel ball, without being in contact with it, by virtue of the field it gives rise to. Which creates an "F", for F=ma, without physical contact.

A photon gives a "kick" to an electron by means of its oscillating electric field (usually, i.e. in electric dipole processes).

9. ### Magical RealistValued Senior Member

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Yes..we went over that chart especially as it pertained to HF, LF, and ELF transmissions. But there was no physics level math or delving into Maxwell's equations. We were just techies, not engineers. Component level trouble shooting, soldering, signal tracing on schematics, test equipment usage, and circuit board swapping was about the whole of it. Then it was liberty call!

Last edited: Mar 4, 2017
10. ### DaveC426913Valued Senior Member

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I asked the Mods to delete some off-topic posts.

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11. ### rpennerFully WiredStaff Member

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There's been some mixing of different physical theories here.

Newtonian Mechanics v. Special Relativity
$\vec{F} = m \vec{a} = m \frac{d\vec{v}}{dt}$ is not a law of nature, it is Newton's definition of a force. Only when there is no net force will bodies move without acceleration.
But non-zero acceleration is tricky in relativity because it depends on one's notion of time in a complicated fashion. Attempts to continue to use this equation in special relativity leads to weird claims that the inertial mass of the body has a speed-dependent mass if you apply the force parallel to the motion and a different speed-dependent mass if you apply the force perpendicular to the motion, which is nonsensical since relativity is the statement that there is no such thing as absolute motion.
So proper treatments of Special Relativity recognize that Newton was really just talking about conservation of momentum (p) and redefine $\vec{F} = \frac{d\vec{p}}{dt}$ which works one way in Newtonian Mechanics and in a different way (compatible with Newton at low speeds) in Special Relativity where the frame-dependent value of momentum for a free body is expressed as:
$\vec{p}^2 = \frac{E^2}{c^2} - m^2 c^2, \; \vec{p} = \frac{ E \vec{v}}{c^2}$
Using simple algebra, if $m = 0$ this is saying: $m = \frac{E}{c^2} \sqrt{1 - \frac{\vec{v}^2}{c^2}} = 0, \; | \vec{v} | = c, \; \vec{p} = \frac{E}{c} \frac{\vec{v}}{ | \vec{v} | } = \frac{E}{c} \hat{v}$
But if $m > 0$, then it follows $m = \frac{E}{c^2} \sqrt{1 - \frac{\vec{v}^2}{c^2}} > 0, \; | \vec{v} | < c, \; \vec{p} = \frac{E}{c^2} \vec{v} = \sqrt{ \frac{E^2}{c^2} - m^2 c^2 } \hat{v} = \left( 1 - \frac{ \vec{v}^2 }{ c^2} \right)^{- \frac{1}{2}} m \vec{v}$
So in Special Relativity, massless bodies traveling at the speed of light can carry non-zero energy and momentum.

Maxwell's equations v. Quantum Electrodynamics
Maxwell in 1865 described the behavior common to experiments with electricity and magnetism and discovered that disturbances propagated changes in forces at a speed faster than any known terrestrial phenomena save one, light. Since then radio confirmed these predictions. QED is a modern synthesis of Maxwell's equations, and Quantum Field Theory (which includes a synthesis of Special Relativity, Quantum Mechanics).
QED deals with details much better when atoms (with quantum effects) and high-frequency light (where per-particle energy is significant).
While Maxwell's equations would say an electromagnetic wave causes electrons to jiggle and jiggling electrons cause electromagnetic waves to be generated, QED describes charged particles like electrons absorbing and emitting photons when this would conserve energy, momentum and angular momentum. This is why somethings are transparent to light: because there is no way photons of the specific energies associated with visible light can be absorbed by a electron bound to an atom without a violation of conservation laws.

Asking classical questions about individual photons is almost always wrong-headed because of the many ways quantum mechanics and quantum field theory enter into the discussion.

QED's origins start with Planck's black body law and Einstein's explanation of the the photoelectric effect. The first says hot things emit light and can be understood as the intersection of QED and Statistical Mechanics.

Classical Thermodynamics v. Statistical Mechanics
So now we want to learn how light makes things warm.

Heat is a way energy presents itself. Thermodynamic equilibrium means every degree of freedom a system has to hold energy has the statistical expectation of holding the same amount of energy (equipartition). So when a beam of light falls on a non-transparent object, some of that energy is absorbed initially as kinetic energy. But physical objects are complicated collections of atoms, so this energy can eventually show up in a chemical reaction, an internal state change of a molecule, a vibration of a molecule, an acoustic vibration, a net separation of atoms in a body, etc. The statical expectation of the measure of any one way the body has of holding energy just got a little higher. That's an increase in heat.

Planck's black body law says the most untransparent objects there are, those that are "black" to every frequency of light, don't just absorb light, but emit it too. (This makes sense because even Maxwell's equations have said that the EM field-electrically charged body relationship is not a one-way one.) So when the details of equipartition are worked out, the object is trying to reach thermodynamic equilibrium with the surrounding electromagnetic field. Human bodies glow in the infrared, electric stove elements and toaster wires glow red, the plasma of the photosphere of the sun is white hot, and some stars are brighter in UV than visible light.

Light from hot things (the Sun, fire, tungsten filament lights, etc) has a broad, smooth spectrum because every frequency gets a chance for equipartition. In contrast, the fluorescent compounds in a light of the same name, low pressure sodium or mercury lights, chemiluminescent reactions, LEDs and lasers use quantum effects of atoms and molecules and bulk materials to emit light which is concentrated strongly at certain frequencies. So hot things glow, but not all things that glow are hot.

Microwave ovens (915 MHz/2.45GHz) and Radar ( 10 MHz - 110GHz) can specifically cause water molecules to torque around in their hydrogen bond networks and transfer motion to nearby molecules. That's why microwaves don't work well on fatty or very dry foods (not enough water/polar molecules) or large solid things (like roast of smallest dimension of 6 cm or more) (microwaves absorbed in outer layers leaving center cold). But this is a bulk electrostatic effect, not related to the free rotation of water molecules. If microwave ovens were tuned to excite the natural rotation frequencies of water, they would not penetrate as far as they do into normal foods.
http://www.schoolphysics.co.uk/age16-19/Wave properties/Wave properties/text/Microwave_ovens/index.html
https://en.wikipedia.org/wiki/Electromagnetic_absorption_by_water

IR and Light can cause intramolecular bonds to vibrate.
Photons carry energy, momentum and angular momentum. Heat is just a name for the incoherent energy of a system which has reached thermal equilibrium. Light in a featureless sealed chamber with the walls all the same temperature is at thermal equilibrium and so we can speak of its temperature. Light with a predominant direction is not at thermal equilibrium, so heat in not a great description for such energy in motion.

Light travels 150 million km from the 5700 K photosphere of the sun through the Earth's atmosphere and a pane of glass to warm your arm held in a sun beam.
The photons are the same frequency as when they left (ignoring GR effects) so have not lost any energy. There are fewer of them than left in your direction because the atmosphere and glass are more nearly transparent to visible light than UV or low frequency IR. The number of photons per square meter of skin is much lower than it would be closer to the sun, because a sphere of radius 150 million km has a much larger surface than one of radius 700 thousand km. So the individual photons have not lost energy, but there's not enough of them to heat you up as hot as the sun.

Last edited: Mar 4, 2017
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12. ### James RJust this guy, you know?Staff Member

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Magical Realist:

Photons carry "electromagnetic energy", if you like. That is, a photon has the potential to create electromagnetic effects on other things, so in that sense it has energy.

Sure. That's what a light intensity meter does.

For example, light from the sun carries about 1340 Watts of power per square meter.

No. An error a lot of people make is to think that energy is like a substance. Energy isn't a substance. You can't have a bottle of pure energy. Energy is always associated with some kind of system.

A photon is the carrier of the electromagnetic field. You can think of a photon as a particle, which is kind of substantial, unlike energy. Nevertheless, there is energy (a number) associated with that particle.

Roughly speaking, its colour, if we're talking about visible light. Of course, we can also have invisible photons in things like x-rays or radio waves.

"Brightness" has a number of different definitions, but most likely you're thinking of something that physicists would usually call "intensity" or "irradiance". The intensity is the amount of radiant energy incident per second on one square metre of area. I gave you an example of the intensity of sunlight above.

There are two ways to increase the intensity, therefore: one is to transfer more energy per unit time, and the other is to pack more energy into each unit area.

In terms of photons, the more photons you get landing on your retina (a fixed area) per second, the "brighter" the light will look (because it has higher intensity).

Individual photons (of a specific colour) have a fixed amount of energy. You can't change the "brightness" of an individual photon of a particular colour. However, you can change the number of those photons that is emitted from a source per second. This is what the dimmer knob on your light switch does.

No. "Heat" has a specific technical definition, which is this: heat is a transfer of energy from a hotter body to a colder body due to a temperature difference between them. "Heat" is therefore not restricted to being a specific "type" of energy. As I said earlier, heat can be transferred by convection, conduction or radiation. Photons, being radiation, can act as one mechanism for transferring heat, but there are others.

It is important to realise that there's no such thing as a "hot photon" or a "cold photon". Photons don't have a temperature - not individually, anyway. Photons are electromagnetic excitations that can transfer energy from one place to another.

Technically, the frequency of a photon determines its energy. Specifically, the energy of a photon is $E=hf$, where $f$ is the frequency and $h$ is Planck's constant.

However, we often talk in terms of wavelengths because frequency and wavelength are related. For photons in free space, $f=c/\lambda$, where $\lambda$ is the wavelength and $c$ is the speed of light. So, in a sense, we can speak about frequency or wavelength interchangeably when we talk about the energy, bearing in mind that high frequency means short wavelength, and vice versa.
I attempted to explain that in my first reply to you.

If you still don't understand, please ask more directed questions rather than simply complaining that things haven't been explained to your satisfaction.

It depends on the details of whether and how those photons interact with the thing they are (potentially) heating. But, in general, yes, probably.

I explained that in my first reply to you, did I not?

The important feature is that when an atom/molecule absorbs a photon, the photon's energy is transferred to the atom/molecule, which then appears in some other form. For example, the kinetic energy of the atom might increase on absorbing a photon. Or, a molecule might vibrate more, or rotate at a higher rate.
Photons carry momentum even though they are massless. A force requires only a transfer of momentum.

That's a special case, in effect. More generally, force = rate of change (or transfer) of momentum.

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