What happens to the temperature of gas in a moving container?

[LameGeek]

Homework Statement

Some gas at 300K is enclosed in a container. Now the container is placed on a fast moving train. While the train is in motion what happens to the temperature of the gas?

Homework Equations

KE(total) = (3/2)(N_A)nkT
KE(avg) = 3/2kT

The Attempt at a Solution

My answer: My intuition tells me that the temperature of the gas would not change.

But I'm a bit confused, since the temperature of the gas is dependent on the kinetic energy of the gas molecules (i.e. increase in their velocity would mean increase in temperature) so wouldn't the container traveling in higher speed increase the velocity of the gas molecules & hence increase the temperature?

Or actually the velocity of the gas molecules is measured relative to the container so whether the container moves or not, velocity of molecules remain the same therefore temperature doesn't change?

 

[phinds]

Your intuition is right in this case. The molecules inside the box are not traveling faster relative to each other by virtue of being on a moving train inside a box, and that's what is meant by "faster" when talking about energy/temperature.

 

[LameGeek]

Thank you so much! Is it right to say that the velocity that determines the KE & temperature of the gas/system is always relative to the container?

 

[haruspex]

Thank you so much! Is it right to say that the velocity that determines the KE & temperature of the gas/system is always relative to the container?

Not exactly.
The distinction usually made is between disordered motion (temperature as an intrinsic property, heat energy as an extrinsic one) and ordered motion (velocity, mechanical energy). What if the air is circulating inside the container as a powerful vortex? You could argue that the vortex motion is ordered, so does not contribute to temperature. In the end, I'm not sure there is no absolute distinction - others may correct me .
Another interesting question is what does it feel like to move through air at various speeds? If the air is colder than you then at modest speeds you get a wind chill effect, but at sufficiently high speeds you would burn up. The relative motion does increase the effective temperature of the air. But bear in mind that at everyday temperatures air molecules move at great speed, so it takes a very high relative motion to make it discernibly hotter.

 

[phinds]

Thank you so much! Is it right to say that the velocity that determines the KE & temperature of the gas/system is always relative to the container?

In the exact scenario you posit, assuming the box is inside a car and absent any external infusion of heat, then yes. The molecules in the box will have no reason to move any faster relative to each other regardless of the speed of the train. This does not invalidate haruspex's comments, but they are not applicable to your specific scenario because there is no ordered motion inside the box.

 

[LameGeek]

Thank you Mr. phinds & Mr haruspex for clearing my doubts! =)