peaceharris said:
CraigD said:
Yes. Both are in the same units as
work, units of

.
No. We can add terms if they have the same dimensions. For example, 1cm+1mm=0.011m. Since you claim energy and temperature have the same dimensions, how much is 1 celcius + 1 Joule?
However, since units of temperature are used only to represent the average kinetic energy of a single particle, and the standard SI unit, K, is very small compared to the standard unit J, adding one of each unit is unusual, and below significance at common levels of precision, as the strange result above suggests.
Some confusion about the units K and J are the result of the convention of not counting “pure” numbers as fundamental physical quantities. So a unit of

is considered the same as a unit of energy.
This is true of all the fundamental and derived physical quantities. For example, we speak of 100 people as massing 7900 kg, or an average person in this ensemble as massing 79 kg – we do not claim that the unit of mass kg cannot be used in both cases.
As temperature is by definition a measure of kinetic energy of an individual (eg: a particle of an ideal gas), this kind of double-use of the same type of unit is especially confusing. Although technically meaningful, it’s weird to refer to a projectile like a bullet as having

rather than 1400 J, or a human being having an oral temperature of

rather than 37° C
If we could not equate temperature and energy, how would it be possible to answer questions such as:
“Inside a vacuum chamber, a projectile massing .05 kg is fired with a speed of 100 m/s into a 1 kg clay target, stopping it. Before the shot, the temperature of the projectile and target are 300 K. After the shot, and allowing time for the target and projectile to reach thermal equilibrium, what is their temperature?”
peaceharris said:
CraigD said:
AFAIK, the main constituent of the interstellar medium, hydrogen, isn’t observed to glow significantly at anywhere near as low a frequency as 160 MHz, peaking mostly in the 750 GHz (7.5e14 Hz, in the high-visible, low-ultra-violet light frequency bands).
How does 750Ghz equal to 7.5e14?
It does not. I made a typographical error. “GHz” should read “THz”. The visible light range of the
EM spectrum is conventionally considered to be between 450 and 750 THz, or

and

cycles/second.
peaceharris said:
Can you give me a reference for this, how exactly it was determined that hydrogen is the main constituent of interstellar medium and how was it determined that it peaks at 750GHz / 7.5e14Hz?
A discussion of the 750
THz peak for hydrogen emission can be found at the
wikipedia article “Balmer Series”
That hydrogen is the main constituent of the ISM has been determined several ways:
- By examining the absorption and emission spectra of starlight and nebulae (Spectroscopy)
- From observation of the relative abundance of elements in the solar system
- As a consequence of cposmological models predicting the relative abundance of the elements
- Via space probes and sample return missions, which directly measure the interplanetary medium, which is assumed to resemble the ISM
This measurement is by no means conclusive, as we’ve not actually sampled the ISM, and spectroscopic data is available only for parts of the ISM lit by background start, but most interested people find it compelling. As the technique has be tested and refined in the lab using artificial gas samples, and because the underlying physics is well understood, the reliability of spectroscopic analysis in determining the composition of gasses is high, so predictions of the composition of the ISM are widely accepted.
peaceharris said:
CraigD said:
So, the average kinetic energy (E) of the particles in an ideal gas at a room-ish temperature of 300 K is

. Assuming the gas in question to be pure nitrogen, each atom of which has mass about 2.32587e-26 kg (M), this gives an average velocity (v) of

The average velocity (a vector) is 0. Assuming this is a typo, the average speed ( a scalar) of nitrogen gas at 300K is still not 597m/s. Try referring a textbook and redoing the calculation. You are using a wrong formula.
You are correct – “velocity” should read “speed” in the quoted text.
I used the usual formula for kinetic energy,

, which is derived from the definition of work,

. Manipulated to solve for speed, it’s

.
My result of 597 m/s matches that of the “molecular speed calculator” at
hyperphysics’s kinetic temperature page.
peaceharris said:
CraigD said:
Yes, but not by much, and only when measured by an observer standing still outside of the train.
So the temperature of an object depends on the frame of the observer. Nonsense.
I wouldn’t call it nonsense, just somewhat useless. Of what possible use is it to know the temperature of a medium in motion relative to you with which you’re not in contact? Even measuring such a temperature would be practically challenging. Nonetheless, a strict interpretation of the physical definition of temperature concludes that the temperature of an object
does depend on its motion relative to an observer.
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