# How is heat stored in bodies?

I'd like to get a general and clear picture of all the ways heat can be stored in a body.

Suppose we have a kiln/furnace in which we put :
particles
a) electrons,...

monoatomic molecules
b) atoms of He...

diatomic molecules
c) atoms of H, O ...

pieces of metal
d) Fe, Cu....

compounf molecules
e) inorganic, H20; organic etc.

I have read that for elementary particles the temperature is considered their KE, that molecules can have also oscillation and rotational thermal energy, can you expand on that?

What happens in the lattice of metals? does the increase of temp affect the motion of electrons?The nuclei cannot translate, do they increase the number od oscillations per sec, or also their rotational speed is affected? I cannot visualize how a particle can vibrate in 3 directions at same time, do you know of any app that simulates and show their thermal motion? Does the frequency od oscillation coincide with the temp? for example if tepm is 100° C, does a nucleus oscillate 373 * kB= 7.77*10^12 times a second?

## Answers and Replies

jambaugh
Science Advisor
Gold Member
The binding between atoms in a crystal lattice should be imagined as if they were linked by springs rather than immovable rigid rods. Here's a youtube video of the analogue model:

As far as vibrating in 3 directions at the same time, the three directions give three components of the single particles single direction of motion at a given instant.

alba
The binding between atoms in a crystal lattice should be imagined as if they were linked by springs
As far as vibrating in 3 directions at the same time, the three directions give three components of the single particles single direction of motion at a given instant.
Thanks for the great applet, jambaugh, I wondered:
do electron react to increase of temp? do the nuclei emit thermal radiation in 6 different directions?
I also do not undersand how molecules can produce EMR by vibrational or rotational energy, doesn't it take an oscillating charge to produce infrareds?

jambaugh
Science Advisor
Gold Member
Yes, the defining difference between heat energy and coherent energy is that the heat energy is randomly distributed among all the degrees of freedom of the system... that will include the electrons bouncing between ground and excited states, and the surrounding EM field being filled with thermal radiation. Imagine a red hot glowing fire poker. The iron atoms are really giggling around, as they bump the electrons get jostled about too and they waggle the EM field so that randomized reddish light is bouncing around everywhere.

If you study it further, there's some beautiful mathematics and physics behind it all too. (1/Temperature as a Lagrange multiplier, negative temperatures, etc.)

alba
Yes, the defining difference between heat energy and coherent energy is

If you study it further, )
Thanks, do you know what is the typical length of oscillation of a nucleus at room temp?
Can you give a link where to expand the difference between heat and coherent energy?

Andrew Mason
Science Advisor
Homework Helper
I'd like to get a general and clear picture of all the ways heat can be stored in a body.

I have read that for elementary particles the temperature is considered their KE, that molecules can have also oscillation and rotational thermal energy, can you expand on that?
Heat flow between systems of particles depends upon the temperature of the respective systems of particles. If the temperatures of two systems are the same, no heat flow will occur between then when placed in thermal contact with each other. That is how we define temperature. According to kinetic theory, If the average translational KEs of two systems in thermal contact with each other (ie. the molecules of each system can physically interact at some common surface), are equal, there will be no net exchange of KE between systems. So kinetic theory tells us that the temperature of a system of particles depends upon the average translational KE of the particles in the system. Rotational and vibrational kinetic energies do not contribute to temperature. That is why monatomic gases have lower heat capacities than diatomic or polyatomic gases.

Elementary point particles have no structure. In order to have rotational or vibrational energy (ie. more than the 3 translational degrees of freedom) particles need to form multi-particle structures that can rotate or vibrate. So elementary point particles that do not interact with attractive forces have only 3 degrees of freedom (all translational). In that case, their KE is all translational (no vibrational or rotational energy).

AM

jambaugh
Science Advisor
Gold Member
Thanks, do you know what is the typical length of oscillation of a nucleus at room temp?
I don't know offhand. You can do a rough calculation in that Boltzmann's constant tells you the average energy per degree of freedom at a given temperature which will be $\tfrac{1}{2} \kappa T$. You would then have to find the interatomic bond strength of the particular material, and the ratio would be the approximate max displacement.
Can you give a link where to expand the difference between heat and coherent energy?
By coherent energy I just mean energy in a known controlled mode. Such as the kinetic energy of a rock in motion resulting from the kinetic energy of each atom of the rock moving in the same direction as every other atom in the rock. The coherent motion of these atoms is what we think of as the rock moving, (or spinning or vibrating in a controlled way) vs random atomic motion which constitutes thermal energy.

In short it is the difference between a marching band and a mob. Coherent=coordinated=orderly vs incoherent = random = thermal. It is also how entropy comes into the picture. Coherent energy is low entropy energy, thermal energy is high entropy energy.