[ 3 / biz / cgl / ck / diy / fa / ic / jp / lit / sci / vr / vt ] [ index / top / reports ] [ become a patron ] [ status ]
2023-11: Warosu is now out of extended maintenance.

/sci/ - Science & Math

View post   
File: 760 KB, 1024x768, penguinbros.jpg [View same] [iqdb] [saucenao] [google]
6365314 No.6365314 [Reply] [Original]

If you accelerate a particle that is at 0K, is it still at 0K or does it have a temperature since it is moving?

>> No.6365341

It can be 0K before and after the acceleration since it's basically the same state. So no, there's no "temperature of motion".

>> No.6365352

>>6365314
Physical movement and th vibration of particles are separate. Just like you can move a vibrating dildo set to the "off" position, and it will remain off even if you move it

>> No.6365364

>>6365314
still 0k, see below

>>6365341
in general 2 observers traveling at different speeds will see the same object as being at different temperatures.

the temperatures are related by
<div class="math"> T = \frac{T_0}{\gamma} = T_0 \sqrt{1 - v^2/c^2} </div>
but since T_0 = 0, T = 0 as well in this case.

>> No.6365391

>>6365352
yea but you could potentially accelerate it in the same way the vibration moves it around, would it still be the same motion?

>> No.6365393

>>6365341
>>6365364
Well shit. I only started relativity this year, but that seems to make sense

>> No.6365396

>>6365314
>>6365352

what if you accelerated it in direction A for t1 and then in direction B (opposite of A) for t2, where t1=t2, and kept repeating that process? Would the object warm up?
Think of it as dildo.

>> No.6365404
File: 327 KB, 1000x907, 1392832985553.jpg [View same] [iqdb] [saucenao] [google]
6365404

>>6365314
a single particle can't be at a temperature. Temperature is a thermodynamic variable only defined for thermodynamical systems at equilibrium.

>> No.6365409

>>6365404
We're talking Newtonian here.

>> No.6365407

>>6365364
but there's an acceleration. your not taking the acceleration into account?

>> No.6365413

>>6365407
Look, if you do a beautifully clean acceleration, say, through gravity, then there's no reason for there to be any agitation.

>> No.6365418

>>6365404
but this is wrong. the temperature of a single particle or molecule exists and is defined such that
the kinetic energy (½mv^2) is equal to 3/2k_b*T, where k_b is the boltzmann consant and T is the temperature.

nanothermodynamics is an entire field devoted to extremely small or singular systems.

>> No.6365429

>>6365413
but since temperature is just the kinetic energy of a particle, surely while its moving it must have temperature. just when its placed down again it doesn't? o_O. or are you saying there's some kind of difference between movement that it attached to heat, and movement associated with movement?

>> No.6365433

>>6365409
what?

>>6365418
No that's wrong. Absolutely, completely wrong. You are throwing together formulas from different context. Internal energy of a statistical ensemble is not the mechanical energy of a particle.
Do you know how temperature, free energy, volume etc. are defined? Both in axiomatic thermodynamics and in statistical mechanics

a particle does not have a temperature just like a single person does not have a GDP

>> No.6365440

>>6365433
if a single particle with high velocity shot into a solid, and bounced off, imparting some momentum, surely the solid's temperature would rise, implying that the particle had a temperature?

?

>> No.6365441

>>6365433
>statistical ensemble
whose talking about stat mech? this is a thread about thermodynamics.

>> No.6365442

>>6365440
temperature is not some kind of conserved quantity, as you seem to implicity use

>> No.6365443

>>6365440
no. it would imply that the process was not reversible.

>> No.6365446

>>6365429
>some kind of difference between movement that it attached to heat, and movement associated with movement
yes, basically when you are in a frame such that the object as a whole is at rest, any other kinetic energy it has it heat.

>> No.6365447

>>6365441
to use thermodynamics, you need to give an explicit construction of basic thermodynamic variables and prove some of their properties consistent with thermo axioms, stat mech is an example of that. If you don't, you're spouting meaningless sentences.
No meaningful definition of T for a single particle has yet been given, for example.

>> No.6365445

>>6365442
ah, true. but it is proportional to the average |KE| of the particles, so why does it stop being proportional to the average KE when there's only 1 particle.

>> No.6365448

>>6365443
only if time only moves forwards

>> No.6365455

>>6365446
ah that makes sense

>> No.6365459

>>6365445
its only proportional for an idea gas, but ok, lets assume it is an ideal gas and move on.

its only proportional to the average of the kinetic energy in the rest frame of the system, normally we assume the system is stationary, but if we want to add movement the correct first law of thermodynamics would be dU = dQ -PdV + udG, where u is the velocity of the whole system and dG is the change of momentum of the whole system. Here you can see we distinguish between the kinetic energy of the whole system and the "extra" kinetic energy. if you only have 1 particle, there is no place for any extra energy since its kinetic energy would be that of the system.

>> No.6365458

>>6365418
>axiomatic physics
LOL! besides everything ought to be the same with n=1, except entropy gets flakier (which goes away as it ought to as you combine particles to bigger systems), no?

>> No.6365464

>>6365458
>>6365458

nope, because there is a movement of the whole system, which is at the exact same KE as the particle. Whereas the |V| of particles in a system with many particles, will have a value, even if the system is not moving.

>>6365459
i'm the guy you just replied to, do i get it now?

>> No.6365472

>>6365464
seems like it.

>> No.6365488

>>6365447
>you need to give an explicit construction of basic thermodynamic variables and prove some of their properties consistent with thermo axioms,
for 1 particle systems we have dV = 0. thus pressure becomes irrelevant, work can be done on a system through some potential like gravitation, T ~ kinetic energy thus heat transfer is just collisions, your equation of state has a potential that is a function of the entropy, which allows heat (kinetic energy) to be changed into potential energy, all processes are reversible, dS for the universe = 0.

there.

>> No.6365500

>>6365433
But it is not wrong. When you talk about the 'statistical ensemble' or classical temperature of a macro substance, you take the average T over all the particles, which is given by the average velocity according to the relation I posted.

If the system consists of only 10 particles, the average is easier to compute. If it is only 1 particle, the average is trivially the temperature of the individual particle.

I know what Im talking about, Ive got an MSc. in Nanotech and there are countless applications that involve single molecule resolution of energy.

A single particle in a cloud of gas has a temperature. This temperature is not necessarily the same as the temperature of the entire system of particles, but that is the greatest probability.

>> No.6365532

>>6365458
yes, thermodynamics is axiomatic. It doesn't just get a little flaky. It simply does not work outside the thermodynamic limit.

>>6365488
I'm seriously wondering if you are high right now. The way you use those symbols and words is absolutely meaningless.

>>6365500
congratulations on your credentials, but temperature is NOT just a constant times an average of a quantity. Especially if the fluctuation of that quantity is not irrelevant with respect to the average itself, which only happens in:

The Thermodynamic Limit

This Ting /sci/ Does Not Seem To Know Anything About

>> No.6365546

>>6365532
>The way you use those symbols and words is absolutely meaningless.
just because you dont understand it doesn't mean its meaningless. for reversible processes thermodynamics is just an energy balance, you seem to be trying to give it all sorts of magical properties then going beyond thermodynamics to statistical mechanics to justify them.

>muh Thermodynamic Limit
that seems to be the only thing you can say about thermodynamics

that other threads about the guy doing classical mechanics from thermodynamics or some shit also ended like this,
>i dont understand thus its word salad
>muh Thermodynamic Limit

>> No.6365565

>>6365546
the thing you call 'temperature' does not act like temperature. You haven't bothered defining it or proving that it has the necessary properties for thermo. 'You don't understand it' is creationist-tier. In the other thread I said the same thing because it was the same thing.

>> No.6365574

>>6365546
You are retarded. Please stop. Please.

>> No.6365582

>>6365565
which properties of temperature arnt satisfied?

>> No.6365589

>>6365582
two interacting system do not reach the same value of 'temperature'

>> No.6365624

>>6365589
>>6365589
the systems are never in contact long enough to reach thermal equilibrium, most of the time everything is adiabatic, if the systems are in contact long enough in means the systems are traveling at the same speed, thus its temperatures are related by T1/m1 =T2/m2, which is the condition for thermal equilibrium in this case. And don't say that equilibrium means that the values must be identical with no constants because mechanical equilibrium through a membrane is an obvious counterexample of that

>> No.6365645

>if the systems are in contact long enough in means the systems are traveling at the same speed

this absolutely does not happen. In almost all interactions between two particles. Scattering, bound states, whatever. Doesn't happen.

It's not even a lorentz-invariant statement, christ.

>> No.6365673

>>6365645
reversible systems also basically never happen, but thermodynamics spends a lot of time describing them.

and hoe is it not Lorentz invariant? 2 things going the same speed at the same point in one frame will do so in any frame

>> No.6365720

>>6365673
you can have processes which are progressively better approximations of reversible processes. And thermodynamics does not discuss solely reversible processes.

Temperature has to reach equilibrium always, after a certain time. Yours doesn't. (It's not the only problem here, but let's focus on this.) Two particles interacting with a newtonian potential (repulsive or attractive), for example, will never reach the same speed in general.

sorry about the lorentz-invariance, I was unclear. I meant the temperature, not the equilibrium

>> No.6365905

>>6365314
question doesn't make sense because temperature is a macroscopic quantity. It only has a meaning for a distribution approximable as infinite