Why does temperature rise with pressure?

russ_watters
Mentor
MoonUnit said:
So, what is actually going on in Bob's scenario? As I see it, the volume decreases, the pressure increases, work was done in compressing it - so the average KE of the particles must be higher - therefore higher T.
Yes.
I'm not doubting you - but I just don't quite get this bit. Maybe I'm missing an assumption here? Is the system exchanging energy with the surroundings as the gas is compressed? If that were happening at a rate which compensates for the work done on the gas, I think I get it.

If not I'm completely perplexed....
Generally, you assume no energy is exchanged with the surroundings - only with the compressor. That's what krab was saying: "adiabatic" means without exchanging heat with the environment. Ie, the only energy input/output comes from the compressor.

LURCH said:
Yes, I'm afraid this is exactly what I am saying. Somebody tell me if I'm way off hear, but if you decrease the amount of area in which a set amount of energy is contained, without adding any new energy, but also without removing any, then the same amount of thermal energy is concentrated into a smaller space. The average amount of thermal energy at any point within that smaller space must therefore be higher. (Theoreticaly, of course, since in practice this would be impossible to do.)
Recognize that temperature is not defined as the average amount of kinetic energy per unit volume. It is the average amount of kinetic energy per molecule. When you compress a gas, you decrease its volume, but you don't decrease its number of molecules. Thus the fact that a compressed gas now occupies a smaller space does nothing to explain why it has a higher temperature.

There is no necessity for an increase in pressure of a gas to cause an increase in temperature if it is paired with a proportionate decrease in volume. The math pretty clearly states that. The ideal case is to examine a container containing just one molecule bouncing around in its merry way. (Credit to Szilard for this idea.) This question becomes much easier to understand when you consider what happens to that molecule when the container's volume is reduced. It's possible for this to even happen without tranferring energy to the molecule. What happens is that you get a molecule that is striking the walls of the container with a greater frequency (pressure) yet still has the same velocity (temperature). Now, this is an ideal case. In the real world, gas heats when compressed because gas molecule speed up when they strike the moving walls of the container as it's shrinking. Even trying to (reliably) only move the walls when no molecules are striking it is going to fail because any attempt to gain that information acts to heat the gas just as if it had been compressed.

WOW !! You people are incredible with this disccusion. Thanks!
I am posting a related question as a new thread about liquefying a gas with pressure.

i believe that the energy of compressing water goes to increasing the vibrational and rotational energies of the molecules and not their kinetic energy. isn't that why water has a higher heat capacity-- and takes longer to heat?

If you apply force to a liquid, wishing to compress it, but it is incompressible, then no work is done on the liquid. No energy is provided to the liquid.

But you have certainly lost some energy, it has gone into your metabolic processes and has been released into the atmosphere. Basically, it has been wasted.

spacetime
www.geocities.com/physics_all/index.html

Jumping into this a couple years late :)

I find it hard to accept that the increase in temperature is only because of a moving surface. The argument seems to be that just like a tennis ball, the molecules bounce off the moving surface (tennis raquet) and increase their speed.

The problem I have is that the speed of the molecules is so much faster than the speed of the surface. It seems to me that the increase in speed that the moving surface imparts would have a very small increase in the temperature. It almost seems like it would be a negligible increase ... 0.00something percent. But as we know the temperature rises quite appreciably.

Consider a propane container used for your standard BBQ grill. As you use the propane with your grill turned on, the container gets very cold. What is happening here? The number of molecules in the container are decreasing. But the walls of the container are not moving? How then are the molecules moving slower if they are not striking a backwards moving surface (as was previously argued). There has to be some component to the change in temperature added by the fact that distances between molecules changes with changing pressure.

Mapes
Homework Helper
Gold Member
I find it hard to accept that the increase in temperature is only because of a moving surface. The argument seems to be that just like a tennis ball, the molecules bounce off the moving surface (tennis raquet) and increase their speed.

The problem I have is that the speed of the molecules is so much faster than the speed of the surface. It seems to me that the increase in speed that the moving surface imparts would have a very small increase in the temperature. It almost seems like it would be a negligible increase ... 0.00something percent. But as we know the temperature rises quite appreciably.
Hi DreadPR, welcome to PF. Yep, this thread is five years old, and some of the original players are no longer active. The moderators may move it to a new thread if they desire.

You need to consider that the same molecule gets many, many momentum-increasing "kicks" as the surface moves inward. (Alternatively, you could calculate how fast the surface would have to move to give an arbitrary molecule just one kick. You'll find it's comparable to the molecular speed.)

Consider a propane container used for your standard BBQ grill. As you use the propane with your grill turned on, the container gets very cold. What is happening here? The number of molecules in the container are decreasing. But the walls of the container are not moving? How then are the molecules moving slower if they are not striking a backwards moving surface (as was previously argued). There has to be some component to the change in temperature added by the fact that distances between molecules changes with changing pressure.
The gas inside the container is doing work on the gas that leaves the container, and thus its temperature decreases, also decreasing the container temperature.

You need to consider that the same molecule gets many, many momentum-increasing "kicks" as the surface moves inward. (Alternatively, you could calculate how fast the surface would have to move to give an arbitrary molecule just one kick. You'll find it's comparable to the molecular speed.)
Thanks for the welcome and the quick response :)

Yes I didn't consider that there would be many many kicks.