Energy source for long-term constant gas pressure?

[KDO2001]

Gas pressure in a closed chamber at constant temperature will last forever, unless leaking or chemical reactions occur. Examples are methane in underground gas reservoirs that are hundreds of thousands of years old. Gases stored in bottles. Pressure comes from the gas atoms (with velocity) colliding with the container walls and other atoms. No collision can be fully elastic and therefore some losses are expected... as it is not a perpetual motion machine. What gives the gas atoms continued momentum/ energy over such long time periods?

 

[Dale]

No collision can be fully elastic and therefore some losses are expected.

Hi KDO2001, welcome to PF!

Excellent question. Why do you think that it would always be the gas that loses the energy and never the container?

 

[moatilliatta]

Pressure comes from the gas atoms (with velocity) colliding with the container walls and other atoms. No collision can be fully elastic and therefore some losses are expected... as it is not a perpetual motion machine.

If these collisions are not elastic, then what do you suggest the energy is converted to? Remember, energy cannot be created or destroyed.

 

[qraal]

Gas pressure in a closed chamber at constant temperature will last forever, unless leaking or chemical reactions occur. Examples are methane in underground gas reservoirs that are hundreds of thousands of years old. Gases stored in bottles. Pressure comes from the gas atoms (with velocity) colliding with the container walls and other atoms. No collision can be fully elastic and therefore some losses are expected... as it is not a perpetual motion machine. What gives the gas atoms continued momentum/ energy over such long time periods?

You've answered your own question - "constant temperature". Inside the Earth, for example, there's a continual heat-flux from the core to the cosmic heat-sink. Any part of the Earth at "constant temperature" is only so because of that constant flux.

 

[KDO2001]

If these collisions are not elastic, then what do you suggest the energy is converted to? Remember, energy cannot be created or destroyed.

I did not think it was possible to have perfectly elastic collisions in nature.

 

[KDO2001]

Hi KDO2001, welcome to PF!

Excellent question. Why do you think that it would always be the gas that loses the energy and never the container?

Either could lose the energy. The container could add energy to the gas, for example rock in the earth. But in a metal bottle on the surface?

 

[KDO2001]

You've answered your own question - "constant temperature". Inside the Earth, for example, there's a continual heat-flux from the core to the cosmic heat-sink. Any part of the Earth at "constant temperature" is only so because of that constant flux.

Yes, that may explain gas deposits in the earth. But it does not explain such pressure maintenance in metal or glass bottles on the surface..

 

[jtbell]

Put your container of gas in outer space, shielded from the sun's radiation. What happens to its temperature (and the average speed of its gas molecules) as time passes?

 

[KDO2001]

Put your container of gas in outer space, shielded from the sun's radiation. What happens to its temperature (and the average speed of its gas molecules) as time passes?

Indeed, in space where radiate losses would allow the temperature to drop to near zero K, pressure would drop per the ideal gas law. Do the gas collisions heat up the container, that then radiates away the energy? But without heat loss to the surroundings (adiabatic) what would happen to the gas pressure? From what I have seen in gas bottles over years, the pressure will be maintained. If that is true for longer terms, then how does that occur?

 

[jtbell]

OK, a container of gas at room temperature (about 300 K) in outer space, radiates in the infrared (or whatever) and cools off.

Take that same container of gas, cool it down to near 0 K, and put it in a room with an atmosphere that is maintained at 300 K. The room radiates into the container and warms it up, right?

Now combine the two situations: a container at 300K in a room at 300K. They both radiate, at equal rates, in opposite directions. The net effect is...

 

[KDO2001]

OK, a container of gas at room temperature (about 300 K) in outer space, radiates in the infrared (or whatever) and cools off.

Take that same container of gas, cool it down to near 0 K, and put it in a room with an atmosphere that is maintained at 300 K. The room radiates into the container and warms it up, right?

Now combine the two situations: a container at 300K in a room at 300K. They both radiate, at equal rates, in opposite directions. The net effect is...

This I do not understand as the two situations are too different. Let's keep simple- A gas is in a completely and absolutely insulated container. What happens to the gas temperature and pressure over time? Both hold steady / constant OR another exchange occurs?

 

[Dale]

Either could lose the energy. The container could add energy to the gas

Exactly. In some collisions the gas will lose energy to the container and in other collusions the container will lose energy to the gas. The temperature difference determines which direction is more likely.

 

[billy_joule]

This I do not understand as the two situations are too different. Let's keep simple- A gas is in a completely and absolutely insulated container. What happens to the gas temperature and pressure over time? Both hold steady / constant OR another exchange occurs?

This is the same situation as:

Now combine the two situations: a container at 300K in a room at 300K. They both radiate, at equal rates, in opposite directions. The net effect is...

In your case no energy can escape, in jtbells case input=output so in both cases the net heat transfer is zero and the temp. & pressure are static.

 

[jtbell]

No collision can be fully elastic and therefore some losses are expected

Also note that collisions between atoms are indeed elastic, unless they are violent enough that the kinetic energy can raise one of the atoms to an excited state. (Substitute "molecule" for "atom" if necessary.) This doesn't mean that the gas atom always has the same KE after a collision with an atom in the wall, as before the collision. Sometimes it has less KE afterwards, sometimes more, depending on the motion of the wall atom before the collision. If the wall is in thermal equilibrium with the gas, the total KE of the gas atoms is effectively constant. More precisely, it has very tiny statistical fluctuations about a constant long-term average.

 

[KDO2001]

Yes, that may explain gas deposits in the earth. But it does not explain such pressure maintenance in metal or glass bottles on the surface..

Upon further consideration, there is no geological evidence that the ground/ formations in the Earth above an underground gas reservoir are cooler than right next to it. Perhaps the difference is so small as not to be noticed. That definitely has not been reported, as it would be a wonderful exploration tool!

 

[KDO2001]

Also note that collisions between atoms are indeed elastic, unless they are violent enough that the kinetic energy can raise one of the atoms to an excited state. (Substitute "molecule" for "atom" if necessary.) This doesn't mean that the gas atom always has the same KE after a collision with an atom in the wall, as before the collision. Sometimes it has less KE afterwards, sometimes more, depending on the motion of the wall atom before the collision. If the wall is in thermal equilibrium with the gas, the total KE of the gas atoms is effectively constant. More precisely, it has very tiny statistical fluctuations about a constant long-term average.

Sorry, I did not know that collisions between low KE atoms are, on average, fully elastic. Thanks for clarifying that point.

 

[KDO2001]

This is the same situation as:
In your case no energy can escape, in jtbells case input=output so in both cases the net heat transfer is zero and the temp. & pressure are static.

Okay. If temperature stays the same, we MUST have perfectly elastic collisions between the molecules and the walls of the container(s). That must therefore confirm perfectly elastic collisions between molecules, which I did not know beforehand. Thanks.

Last question, at what molecule size do the collisions become inelastic, if ever? Or are all molecular collisions perfectly elastic?

 

[Dale]

If temperature stays the same, we MUST have perfectly elastic collisions between the molecules and the walls of the container(s).

Not necessarily. All you need is that the energy transfer from gas to wall must be equally likely as the energy transfer from wall to gas.

 

[stedwards]

To balance the energy, we have both molecules and radiation. The gas molecules can be in an excited states which can be thought of as either kinetic or potential. Solids will have lattice energy.