What is the temperature of a body ? " Temperature is a physical property of a system that underlies the common notions of hot and cold; something that is hotter has the greater temperature. Temperature is one of the principal parameters of thermodynamics. The temperature of a system is defined as simply the average energy of microscopic motions of a single particle in the system per degree of freedom. For a solid, these microscopic motions are principally the vibrations of the constituent atoms about their sites in the solid. For an ideal monatomic gas, the microscopic motions are the translational motions of the constituent gas particles. For multiatomic gas vibrational and rotational motion should be included too. " So, if the temperature is a measure dependant on average kinetic energy, will it be frame dependant like kinetic energy ? To illustrate, consider a closed massless container filler with an ideal mono-atomic inert gas. Let its average kinetic energy be E. Let is also be rest with any frame of referance A. According to the kinetic theory of gasses, the molecules inside the gas will experience random motion in all directions. This will contribute to heat and in turn temperature. Let its temperature be T1. Since there is no external force acting on this adiabatic and closed system, its center of mass be at rest. Now, consider frame of referance B : Sit on any one molecule. From this frame, the velocity of the molecule becomes zero and hence so does its kinetic energy. If there are other molecules with the same energy, they will now also have no kinetic energy. In this new frame of referance there is another problem, the center of mass has some velocity. As a result the net kinetic energy of the container changes in this new frame of referance. But will also the temperature ??? It is against classical mechanics for such a thing to happen. Considering very small temperatures, and speeds NOT approaching c, how can this problem be solved. The temperature of a substance MUST be the SAME in any frame of referance. But, if it depends of kinetic energy = 1/2mv^2 and that depends on velocity with varies with frame of referance, it is deducable that so is temperature. HOW can this be explained?
Avg Kinetic energy When thinking of the monoatomic ideal gas, the temperature becomes proportional to the average kinetic energy of the molecules. You must keep in mind for a container with 3 degrees of freedom there are many atoms (in the order of 10^23). If you are sitting on the one atom as it traverses around the container the the other atoms are not all traveling parrallel the ones traveling opposite seem to have twice the KE while the atoms traveling parrallel appear to have no KE. Due to the large number of atoms the KE averages out.
My understanding is that temperature of an object is based on the average kinetic energy of its particles in one reference frame only - the frame in which the object is at rest (the frame in which the average momentum of the particles in zero). I'm not sure that your quoted definition (from Wikipedia?) is complete. The same article also mentions other definitions of temperature: ...if two systems, A and B, are in thermal equilibrium and a third system C is in thermal equilibrium with system A then systems B and C will also be in thermal equilibrium ... Since A, B, and C are all in thermal equilibrium, it is reasonable to say each of these systems shares a common value of some property. We call this property temperature. ...the temperature in kelvins is the pressure in pascals of one mole of gas in a container of one cubic metre, divided by 8.31... ...The reciprocal of the temperature is the rate of increase of entropy with energy. In this context, I think the first in that list is the most relevant, and dictates that temperature must be frame independent. Consider two objects in contact, sliding past each other frictionlessly. If the two objects are in thermal equilibrium, then it's obvious that they must be in thermal equilibrium in all reference frame - you can't have heat flowing one way in one frame, but not another. This implies that the two objects are the same temperature in all reference frames, and that temperature must be frame independent.
In reply to Vern, I made some comments about temperature here: http://www.sciforums.com/showpost.php?p=1440486&postcount=20 This thread has not yet recognized that temperature can also be well defined for a radiation field {(2) below.} but, if one is precise, hardly ever does temperature exist. (Thermal equilibrium is rare.) At above link I said: "...Pyroelectric fusion does not occur at any "temperature." Temperature is a concept associated with either (1) a "thermal distribution" of kinetic energy in the particles of some mass, OR (2) an omni-directional* radiation field with the distribution of photons (or their energy depending on which way equation is written) given by Planck's law equation (where the sole parameter in that equation, T, is the temperature.) Pyroelectric fusion is very very different (hard to imagine any greater separation) from either (1) or (2) and thus does not have any temperature. ..." After this, I went on to explain why extremely few collisions in the fusion core of sun cause fusion. (Vern had called our attention to new and confirmed form of "cold fusion", but was not careful enough [for me] with his use of the concept of temperature.) There were some things about the solar fusion mechanism, I have forgotten, and asked if any one could supply (at the above link). I want to emphases that temperature is NOT the "average kinetic energy in the center of mass frame", except when those particles have the Maxwell/ Boltzman distribution of their particle energies. Wiki not only neglects the fact that radiation alone can have a temperature, but from what I see posted here, the requirement for this distribution and thermal equilibrium! ---------------------- *Some might omit the "omni-directional requirement", but I think it is necessary as without it the concept of thermal equilibrium in the definition of temperature collapses.
Crudely but true, temperature is a measure of an "affinity" to attract heat. The higher temperature the less affinity. Another word for heat is "energy", i.e. temperature is a measure of body's affinity to attract energy. T=1/(dS/dU)n,V S - enthropy - energy being dispersed U - internal energy All proceses in the nature occur in such a way so the amount of the dispersed energy is maximal (second law) Therefore, (dS/dU)n,V is an expression for "heat affinity" of a body with fixed volume and N. The greater "dispersive" properties of a body the larger dS/dU, the smaller body's temperature. Since concept of energy is highly intuitive and cannot be defined in a non circulatory way, since second law is a law not a theorem, I'm afraid we just stuck with temperature. It's just there, it just exists, we will never be able to understand/explain it, as we cannot explain space and time.
