Renge Ishyo said:
Chronos already provided a link which gave multiple definitions for the word "temperature" and concluded that there was no established one. The wikipedia is not universally considered to be the final word on physics definitions.
Actually, you have to go a bit deeper than the standard definition of temperature to find out what limits it. The definitions for temperature ARE vauge (even the one on wikipedia). However, temperature's definition no matter where you look depends on heat, and heat is a concept directly related to internal energy. It is the definition of internal energy that limits what the term temperature can encompass, that term is not defined for particles below the molecular level (since it is a generalization that stands for the sum of all energy processes taking place below the molecular/atomic level). Unless you can find a defintion of internal energy that contradicts that?
That is a myth...His 1905 derivation is wrong and the formula was already known before for radiation by other people.
I wouldn't be surprised, but at the same time my understanding is that Einstein did do a binomial expansion that included the rest energy of matter in it sort of as a sidenote (people discovered the signficance of it completely independant of Einstein?). Either way, if we argue about definitions and can't get our story straight you don't even want to touch history.
If your refer to this link http://www.temperatures.com/wit.html
I would say that definition (initial and point 5 on website) is restrictive. Other beliefs about temperature are wrong. The wiki is not a good reference also.
The link initially refers to the concept of energy in ideal gases. That is, gases of molecules without internal structure (pointlike ones) and with a rigid spheres intermolecular potential. In that restricted case (
and only then) T is
A measure proportional to the average translational kinetic energy associated with the disordered microscopic motion of atoms and molecules.
the concept of temperature is related but not restricted to heat. I heard in this thread that temperature is "not defined" or "ill-defined". This is not correct, the only definition of temperature (axiomatic one) is
<br />
\frac{1}{T} \equiv \frac{\partial S}{\partial U}<br />
Note that the concept of heat is not directly invoked in the definition.
Above definition when applied to an ideal gas recovers the kinetic temperature which is defined on translational motion only.
Temperature, as already said is valid "elsewhere". Has a single atom temperature? Of course.
Take a macroscopic system at equilibrium. It is at T. A system is at equilibrium if you split it into two parts and each part has temperature T. Doing this spliting again one obtains that the temperature of a single atom in the systems is T. Formally this follows from the
extensive property of both internal energy and entropy.
In fact for a system at equilibrium one has
<br />
\frac{1}{T} = \frac{S}{U}<br />
and if one works in the "field representation" of thermodynamics (TIP)
<br />
\frac{1}{T} = \frac{S}{U} = \frac{\rho _{S}}{\rho _{U}}<br />
where the "rhos" are densities (field quantities) which follows from extensive property. Working at molecular level, one can write
<br />
\frac{1}{T} = \frac{S}{U} = \frac{s}{u}<br />
which also follows from extensive property. s and u are molecular (atomic or particle) quantities verifying the extensive property. for example.
<br />
U = N \ u<br />
with N the total number of molecules (atoms or elementary particles).
regarding E = mc^2 simply to say that Einstein derivation is restrictive and wrong and formula was obtained before by other people (e.g. Poincaré) therefore there is an idea of Einstein plagiarized Poincaré works. A thesis sustained by Einstein claim that newer read work of Poincaré and Lorentz when historical evidence says the contrary.
On any case, the formula, in its modern sense, is atributed to Poincaré.
Maybe you guys will find some experimental evidence someday that conclusively proves that light (for example) can gain and lose heat/temperature as it travels through space independent of any kind of interaction with molecules (hence, conclusively proving that it behaves identically to temperature and the transfer of heat as they are defined in thermodynamics). If/when you can do that, I'll owe you both a drink.
I wait in 15-50 days).
