# Temperature of gas in accelerating container

This is a question whose different versions have been asked here a couple of times, but I don't find a clear answer.

• Does the temperature of a gas increase on accelerating the container?

• What happens if the acceleration is negative?

I can think of the fact that when a container is under uniform motion (no acceleration), the gas molecules inside are moving due to their Brownian Motion, but also, due to the container's movement. Both of these contribute to the gas molecules' kinetic energy. But I can't figure out what happens when the velocity of the container is increasing (or decreasing, as in negative acceleration).

We can assume the container to be rigid and its walls to be adiabatic. We also assume the postulates of the Kinetic Theory of Gases to be true.

I would appreciate a qualitative explanation instead of one that involves mere formulae.

• The situation with positive and negative acceleration would be the same, considering symmetry. May 28 at 9:57
• Is it accelerating from rest, or has the acceleration been going on for a long time? If the former, are you interested in the initial transient changes? May 28 at 10:58

Considering the symmetry first, the result of the two operations is the same. I think if the acceleration continues, the temperature will increase. We can think as follows. When the acceleration is large, since a mass of gas is not a rigid body, under the action of inertia, this mass of gas is being squeezed, so the temperature increases.

• Would the gas really be squeezed? Pressure should be higher at the rear end, but lower at the front, right? May 28 at 12:26

If the acceleration is constant, aside from an initial transient, when the system reaches thermal equilibrium, the temperature is no longer changing with time even if the container is still accelerating. By Einstein's equivalence principle, it is the same as if the gas were at static equilibrium within a gravitational field featuring a gravitational acceleration of the same magnitude and opposite direction to the acceleration of the container (and gas).

Gas molecules have mass and mass has inertia.

In the case of initial acceleration, when the front of a container of gas accelerates the inertia of the molecules resists forward motion resulting in them piling up (compressing) towards the rear of the container and spreading out at the front of the container. In effect, the molecules towards the front of the container lose energy doing work compressing the molecule towards the rear which gain energy. This results in a rise in the temperature of the gas towards the rear and decrease in the temperature of the gas towards the front. But the average random KE of all the molecules and thus its total internal energy does not change (since the container is both adiabatic and rigid).

In the case of initial deceleration, the same occurs except the rise in temperature is towards the front of the container and drop towards the rear.

After the acceleration has gone on for a long time, there is no further piling up and spreading out of the molecules so the temperatures remain constant, i.e., a constant temperature gradient exists between the front and rear of the container.

Hope this helps.