Relativistic Thermodynamics

>>9105168
If you have a box with a relativistic non interacting gas in it, the average kinetic energy of the particles will be higher than the one of the same system but with non relativistic particles. So the temperature would be higher too (kT = Ekin, with k being the boltzmann constant). It doesn't make sense to decouple speed and T.

If you're thinking of the thermodynamics of liquids and solids, it instead doesn't make sense to speak about relativistic speeds.

>>9105168
>However since the mass is increasing, their speed has to decrease
>Thus as the entire system approaches light speed

see the problem?

>>9105308
I do not. Could you elaborate? Or maybe I can:
By increasing mass I mean both the mass of the particles as well as the system, the first speed is regarding the particles and the second regarding the system.
As the speed of the system approaches the speed of light, the mass of the particles approaches infinity. Since there is no energy added to the particles themselves their momentum should stay the same, which means their speed has to drop.

>>9105242
Correct me if Im wrong but temperature is not absolute speed, but only speed of particles relative to each other.
If you look at a single particle, its momentum (relative to other particles around it) should be constant during acceleration, while the mass increases due to relativistic effects. This can only mean that the speed of the particle has to decrease, which since it happens to all the gas particles, means that the temperature drops.

>>9105483
Particle speed is unrelated to the system speed.

>>9105496
Particle mass should still increase at high system speeds just due to special relativity.

>>9105483
>Correct me if Im wrong but temperature is not absolute speed, but only speed of particles relative to each other.

In the case of the perfect gas it is the absolute speed, or if you prefer the absolute speed referring to the laboratory system of reference. Particles don't see each other.

Apart from this, the while concept of "relativistic mass" is generally thought to be pedagogically wrong. A system has a fixed mass, the rest mass, and you need infinite energy to bring it to speed c.

>>9105514
>The word "mass" is given two meanings in special relativity: one ("rest mass" or "invariant mass") is an invariant quantity which is the same for all observers in all reference frames; the other ("relativistic mass") is dependent on the velocity of the observer.

>>9105524
>In the case of the perfect gas it is the absolute speed
Are you sure about this? Because Im pretty sure that temperature has nothing to do at all with the absolute speed of the system that the particles are part of, but only with their speeds relative to each other.

Maybe this is a better approach: what temperature would you say does a system moving at the speed of light have? At that point it would definitely be impossible for the particles to move relative to each other, since some of them would be moving faster that C which is not possible.
Would it not then make sense for the temperature to gradually drop towards absolute zero, the faster you go?

>>9105541
You do realize you put in energy to the system and assume it's conserved right?

>>9105546
I know Im putting energy into the system by accelerating it. However that energy should in no part go towards increasing the momentum of the particles, and instead only towards increasing the momentum of the system itself.
If you know for a fact that some of the energy ends up as thermal energy then Id love to see the source for it.

Regardless of that energy, the point about light speed temperature still stands: what other temperature could the system have than absolute zero?

>>9105555
Thermal energy =/= average kinetic energy

>>9105559
Have you ever had an actual lecture on thermodynamics? Because as far as I remember that is exactly what thermal energy is.

>>9105561
Nope. It's TOTAL kinetic energy. Average = temp.

>>9105568
God dammit you made me mix them up. Individual particle speed combined from all particles is temperature.
That means that my point stands though.

>>9105639
>individual speed is a function of temperature
>mass is invariant sans observer relativism
>more energy = more speed = more temperature
Your point, my lad, stands in a pile of shit.

>>9105655
How the fuck are individual particles supposed to move if the system moves at C? You havent answered this yet.
And most likely: they cant. And they dont.

>>9105695
The laws of physics are invariant under coordinate transforms. From the frame of reference of the box with the particles moving in it, everything proceeds exactly as normal - the particles bump around exactly as they did before.

From the frame of reference of an observer watching the box sail past at almost [math]c[/math], a clock on the box would seem to be running slow, so the particles would also seem to be moving about the box more slowly. I'm a little rusty on my general relativity so this might just be my unfounded intuition talking, but I think the resulting apparent increase in mass and decrease in apparent velocity of the particles should maintain the 'thermal' momentum. The box and particles will of course also gain a massive amount of momentum in whatever direction the acceleration was, but if the box and every particle are accelerated at exactly the same rate it shouldn't affect their relative thermal motions at all.