# Frame dependence of temperature

## Main Question or Discussion Point

Is temperature frame dependent?

The temperature of the system is due to the translational,rotational and vibrational movements of the particles of the system

Now if a box containing gases at a certain temperature is accelerated the molecules in the direction of motion of the gases get more velocity therefore on an average the KE increases this leads to increase in internal energy and finally increase in the temperature.

But i've heard people saying temperature is independent of the frame velocity .
so which is correct??

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Suppose a box of ideal mono-atomic gas has reference frame velocities vxav, vyav, and vzav. Then at equilibrium the atoms of the ideal gas have these three average velocities. Now define the rms (root mean square) velocities as

vx rms = sqrt[sum over all atoms (vx - vxav)2]/N, et seq. for y and z. where the sums are over N = billions and billions of atoms.

The "thermal temperature" of the gas is given by vx rms et seq, and not by vxav et seq., and therefore has no direct connection to the reference frame velocity.

Suppose a box of ideal mono-atomic gas has reference frame velocities vxav, vyav, and vzav. Then at equilibrium the atoms of the ideal gas have these three average velocities. Now define the rms (root mean square) velocities as

vx rms = sqrt[sum over all atoms (vx - vxav)2]/N, et seq. for y and z. where the sums are over N = billions and billions of atoms.

The "thermal temperature" of the gas is given by vx rms et seq, and not by vxav et seq., and therefore has no direct connection to the reference frame velocity.
This is strange bob, you see the Vxrmswould not be zero !
because the maxwell - boltzmann distribution function shows that all the molecules don't go on randomly the momentums of the molecules can be diverse in the x,y,z directions so at any instant the Vx-vxav^2 would be the sum of all the molecules in the x direction.
Try to relate Consider this 1+1+1+1+.......+n/n would not be zero but would not be zero .
but 1
If the one you said was zero
then the rms velocity would have never been before us!!

To get it Simple ....
suppose a ball is floating in the mid air in the train.
when the train acclerartes the ball would be fixed to the reference frame of the train.
It would not be just floating in air even if the train moves for an observer outside it would have a pseudo force on it.
anything in the train is always connected to the train!

This is strange bob, you see the Vxrmswould not be zero !
because the maxwell - boltzmann distribution function shows that all the molecules don't go on randomly the momentums of the molecules can be diverse in the x,y,z directions so at any instant the Vx-vxav^2 would be the sum of all the molecules in the x direction.
Here is the recipe for calculating the rms molecular velocity distribution about the average velocity on a train. We consider only the x direction, which is the direction the train is moving.
Get a 1 liter box
Count the number of molecules N in it (about 2.7 x 1022)
(Note: this will take a long time)
Measure the x velocity vx for each molecule
Add vx for all N molecules & get sum(vx)
Calculate average velocity vav = sum(vx)/N
For each molecule get mean square deviation from average (vx-Vav)2
Sum over all N molecules =sum(vx - Vav)2
Take square root
sqrt{sum(vx-vav)2}
Divide by N to get root mean square velocity vrms
vrms = [sqrt{sum(vx-vav)2}]/N
Does this depend on the velocity vx of the frame (moving train)?