Understanding Heat Energy: A Comprehensive Explanation from Basic Physics Books

[Farn]

All the basic physics books I've read explain heat as particles in motion. This means a hot chunk of matter is simply one which has its particles bouncing around more rapidly than a cooler chunk.

I accepted this description for awhile. However, since I started to think about it more, It would seem to me that the idea of 'bouncing' particles is probably a very simplified one. For instance, what would a single hydrogen molecule (atom) floating in space look like if it had more or less heat energy?

So basically what I'm asking for is a more detailed explanation of heat...?

 

[Ivan Seeking]

Originally posted by Farn
All the basic physics books I've read explain heat as particles in motion. This means a hot chunk of matter is simply one which has its particles bouncing around more rapidly than a cooler chunk.

I accepted this description for awhile. However, since I started to think about it more, It would seem to me that the idea of 'bouncing' particles is probably a very simplified one. For instance, what would a single hydrogen molecule (atom) floating in space look like if it had more or less heat energy?

So basically what I'm asking for is a more detailed explanation of heat...?

Very astute Farn.
There is a deeper idea that uses the number of "degrees of freedom" for a given molecule or atom. For a monatomic molecule [atom or ion] there is only translational motion. For a diatomic molecule, like hydrogen, we can imagine the molecule as having a dumb-bell shape. We can have rotation about any of the three axes. However the energy stored in the rotation about the length of the bell would be negligible as compared to the other two axes. So, if we ignore the one axis, and then add the term for normal translation [eg linear motion], we have three significant terms that contribute to the total thermal energy capacity of the molecule.

Through the "law of equipartitions", for a diatomic molecule like hydrogen, and for one having translational motion, we can write the molar heat capacity of the gas as:
3n((1/2)RT) + 2n((1/2)RT) = (5/2)nRT = molar heat capacity U

Note the additional term of 2n((1/2)RT for U.

Since the Specific Heat at constant pressure C_p, and the S.H. at constant volume C_ν, have a difference equal to the ideal gas constant R, we can calculate the specific heats for a gas this way.

Edit: Of course the best explanation for this gets much more complicated, but this is the next level of interpretation from the one that you describe. Also, we can't consider the rotation of the nucleus of the atom about its axis because at this level, the nucleus is assumed to be a point.

 

[quartodeciman]

I would suppose a "hotter" free atom would have a greater speed.

But there is more to heat than just atomic/molecular motions. There is electromagnetic flux, or if you prefer, photon flux. Of course, hot active atoms can produce this heat in the form of radiation. But here is an interesting special case from solar physics.

The temperature of the solar atmosphere above the photosphere (, where opacity drops off) suddenly starts increasing, until it hits 1 million K in the corona. The corona is an extension to the sun's atmosphere that helps produce the solar wind that reaches earth. The corona has a very tenuous (low) gas density. Some of the atoms in it produce light frequencies when their electrons drop from metastable levels. That means the atoms are left alone by other atoms long enough for the electron to make the drop after a sufficient delay. Why this high temperature? The radiation flux from the photosphere mostly travels through the corona out into space and become sunlight. If the corona really had a high matter-radiation equilibrium temperature, it would glow at visual and UV frequencies with such intensity that the sun itself would be completely hidden. Instead, the corona is only visible to us during total eclipses. Yet the corona emits xrays, and much more strongly than the solar atmosphere below. That indicates a very high temperature. So, corona has low density of emitters but very high temperature, according to the ionization states of its constituent atoms. There are theories about about this, but no sense of completion.

Here is some stuff to explore. links --->

http://science.nasa.gov/ssL/pad/solar/corona.htm

UCAR:the solar corona - movies

NASA:how is the solar corona heated?

from Prof. Paul J. Wiita, GSU Astronomy 1020 lecture:

THE SOLAR ATMOSPHERE

PHOTOSPHERE: visible, IR and UV continuum radiation streams out from here. Thickness about 400 km 4500 < T < 5800 K; usually say T_s = 5760 K density between 10^{-5} and 10^{-8} g/cm^3 emerging spectrum is continuum (from dense lower layer) with superposed absorption lines (from less dense, cooler outer layer)

CHROMOSPHERE: mostly UV emission line radiation
Irregular thickness, averaging 5000 km in SPICULES 4500 < T < 10,000 K (up to 50,000 K in transition zone) density averages around 10^{-10} g/cm^3 only visible when photosphere is obscured

CORONA: mostly X-ray emission Irregular thickness, typically out to 2-3 times Solar radius Average T = 1 x 10^6 K extremely low density only visible when photosphere is obscured or via X-ray telescopes heated via magnetic energy orginating in the convective zone of the sun: probably by both magnetohydrodynamic shocks and magnetic reconnection.

WIND: small amount of matter boiled off CORONA
Typical speed, 500 km/s (roughly the Sun's escape velocity) Mostly protons, Helium-4 nuclei (also called alpha particles) and electrons Continually hitting Earth's magnetosphere
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Why is the solar corona so hot, and what does that heat mean? That gets me back to your question.

 

[Tyger]

Temperature is mean free energy per unit quantum, although expressed in different units, regardless of the nature of the quantum. Heat is basically a measure of the total free energy of a thermodynamic system. It can be a measure of potential as well as kinetic energy.

 

[Chi Meson]

In the midst of these good answers, I have to insert a short semantic note here:

The proper term for this thread is "internal energy" (aka "thermal energy," but the former is more correct [see the previous note]).

"Heat" is specifically the amount of this internal energy that is transferred into or out of a system.

"Temperature" is a unitless, artificial number that is proportional to the average amount of kinetic energy per particle in a chunk of stuff.

Since "temperature" is only meaningful in the macro world (large amounts of molecules and atoms in a system), a single atom of hydrogen cannot have a "temperature" and therefore could not be considered "hotter" or "colder."

But enough with splitting hairs! The only significant kind of energy a single ground-state hydrogen atom could have is linear kinetic. So, as was already said, a "hotter" hydrogen atom is moving faster than a "cooler" one.