# Do molecules attempt to align their electric dipole along the steepest energy density gradient?

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Molecules have a probability of direction of emission relative to their electric dipole moment, with maximum probability perpendicular to their electric dipole moment, and zero probability parallel to their electric dipole moment.

For graybody objects, there is also a probability of emission based upon the energy density gradient, with maximum probability along the steepest energy density gradient and zero probability with zero energy density gradient.

The electric dipole moment is an EM phenomenon, and the energy density gradient is an EM phenomenon... so is there some mechanism by which polyatomics attempt to align themselves with their electric dipole moment perpendicular to the steepest energy density gradient, to maximize radiative emission (even though it's likely disrupted by continual random thermal vibrations), knowing that systems always seek their lowest energy state and attempt to do so along the steepest gradient?

Sort of like how a magnet orients itself along magnetic lines of flux.

The reason I ask is if we were able to control the orientation of the electric dipole moment in a material, we could turn radiative emission off (turn the molecule so its electric dipole moment is parallel to the emitting surface) and on (turn the molecule so its electric dipole moment is perpendicular to the emitting surface). A 'heat switch'. We could also align all electric dipole moments perpendicular to the emitting surface to maximize radiant exitance.

What do you mean by "energy density" in objects? Are your objects uniform or no?

The radiation source in objects is not obligatory the electric dipole momentum of molecules.

I'm asking if two different things are somehow connected:

1) the probability of emission direction in relation to the electric dipole moment (highest perpendicular to it, zero parallel to it)...

2) the probability of emission according to the energy density gradient (highest along steepest gradient, zero along zero gradient)

What I was wondering was whether the electric dipole moment attempted to align along the steepest energy density gradient, nature's way of achieving the lowest energy state in the shortest time possible with as little effort as possible?

It doesn't matter whether the objects have uniform energy density.... energy does not and cannot flow without an energy density gradient. Nothing happens without a gradient of some sort, anywhere in the universe.

As regards energy density and energy density gradient:

There are two forms of the Stefan-Boltzmann (S-B) equation:

[1] Idealized Blackbody Object form (assumes emission to 0 K and ε = 1 by definition):
qbb = ε σ (Th4 - Tc4)
= 1 σ (Th4 - 0 K)
=    σ  T4

[2] Graybody Object form (assumes emission to > 0 K and ε < 1):
qgb = ε σ (Th4 - Tc4)

It should be noted that idealized blackbody objects don't actually exist... they're idealizations. The best we can do is laboratory blackbodies which exhibit high absorptivity and emissivity in a certain waveband, but even they are not really idealized blackbodies because they have thermal capacity. Remember, an idealized blackbody object must absorb all radiation incident upon it, and must emit all radiation it absorbs, so it cannot have thermal capacity. Thus we should be using the graybody object form of the S-B equation in all circumstances.

Temperature (T) is equal to the fourth root of radiation energy density (e) divided by Stefan's Constant (a) (ie: the radiation constant), per Stefan's Law.

e = T4 a
a = 4σ/c
e = T4 4σ/c
T4 = e/(4σ/c)
T = 4√(e/(4σ/c))
T = 4√(e/a)
where:
a = 4σ/c = 7.5657332500339284719430800357226e-16 J m-3 K-4
where:
σ = (2 π5 kB4) / (15 h3 c2) = 5.670374419184429e-8 W m-2 K-4
where:
σ = Stefan-Boltzmann Constant
kB = Boltzmann Constant (1.380649e−23 J K−1)
h = Planck Constant (6.62607015e−34 J Hz−1)
c = light speed (299792458 m sec-1)

σ / a = 74948114.502437694376419756266673 W J-1 m (W m-2 / J m-3)

-------------------------

The traditional Stefan-Boltzmann equation for graybody objects:
q = εh σ (Th4 – Tc4)

[1] ∴ q = εh σ ((eh / (4σ / c)) – (ec / (4σ / c)))

Canceling units, we get J sec-1 m-2, which is W m-2 (1 J sec-1 = 1 W).
W m-2 = W m-2 K-4 * (Δ(J m-3 / (W m-2 K-4 / m sec-1)))

[2] ∴ q = (εh c (eh - ec)) / 4

Canceling units, we get J sec-1 m-2, which is W m-2 (1 J sec-1 = 1 W).
W m-2 = (m sec-1 (ΔJ m-3)) / 4

[3] ∴ q = (εh * (σ / a) * Δe)

Canceling units, we get W m-2.
W m-2 = ((W m-2 K-4 / J m-3 K-4) * ΔJ m-3)

One can see from the immediately-above equation that the Stefan-Boltzmann (S-B) equation for graybody objects is all about subtracting the energy density of the cooler object from the energy density of the warmer object.

The Stefan-Boltzmann equation in energy density form ([3] above):
σ / a * Δe * εh = W m-2

σ / a = 5.670374419184429e-8 W m-2 K-4 / 7.565733250033928e-16 J m-3 K-4 = 74948114.502437694376419 W m-2 / J m-3.

That's the conversion factor for radiant exitance (W m-2) and energy density (J m-3).

The radiant exitance of graybody objects is determined by the energy density gradient.

Energy can't even spontaneously flow when there is zero energy density gradient:

σ [W m-2 K-4] / a [J m-3 K-4] * Δe [J m-3] * εh = [W m-2]

σ [W m-2 K-4] / a [J m-3 K-4] * 0 [J m-3] * εh = 0 [W m-2]

... it is certainly not going to spontaneously flow up an energy density gradient.

Note 2LoT in the Clausius Statement sense:
"Heat can never pass from a colder to a warmer body without some other change, connected therewith, occurring at the same time."

'Heat' [ M 1 L 2 T -2 ] is definitionally an energy [ M 1 L 2-2 ] flux (note the identical dimensionality), thus equivalently:
"Energy can never flow from a colder to a warmer body without some other change, connected therewith, occurring at the same time."

That "some other change" typically being external energy doing work upon the system energy to pump it up the energy density gradient, which is what occurs in, for example, AC units and refrigerators.

Remember that temperature is a measure of energy density, equal to the fourth root of radiation energy density divided by Stefan's Constant, per Stefan's Law, thus equivalently:
"Energy can never flow from a lower to a higher energy density without some other change, connected therewith, occurring at the same time."

Or, as I put it:
"Energy cannot spontaneously flow up an energy density gradient."

My statement is merely a restatement of 2LoT in the Clausius Statement sense.

-------------------------

Do remember that a warmer object will have higher energy density at all wavelengths than a cooler object:

This next URL gets broken by the website's code interpreter... join together the two URLs to load it from the Wayback Machine.

https://web.archive.org/web/20240422125305if_/

... so there is no physical way possible by which energy can spontaneously flow from cooler (lower energy density) to warmer (higher energy density).

Because every action in the universe requires an impetus... that impetus being a gradient of some sort. Actions don't spontaneously occur against the gradient, or with zero gradient.

Energy can't even spontaneously flow when there is zero energy density gradient:

It is a wrong statement. It is just on the contrary: at $T\gt 0$ the radiation flows out in all directions and comes from all directions inside a body even at a uniform temtemperature. The notions of temperature and the energy density are statistical, average, mean, not microscopical. There are always their fluctuations, so spontaneously there are fluctuations of the radiation.

When $T_h =T_c$ there are two equal but the opposite energy flows. Therefore, the "dipole momentums" are not aligned according to the energy density gradient.

"It is a wrong statement. It is just on the contrary: at > 0 the radiation flows out in all directions and comes from all directions inside a body even at a uniform temtemperature. "

No... you've forgotten about entropy. In order for your claim that energy flows at all temperatures > 0 K to be true, entropy at thermodynamic equilibrium (TE) wouldn't change because radiative energy transfer would be an idealized reversible process... except we know that radiative energy transfer is an entropic irreversible process.

At TE, no energy flows, which is why entropy doesn't change. The system reaches a quiescent state (the definition of TE). The only reason why emissivity and absorptivity must be equal at TE (Kirchhoff's Law) is because both are zero. I encourage you to read here (especially the parts about cavity theory and energy density gradient) for why what you state cannot reflect reality:

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