Cooling that is both Adiabatic and Isochoric - possible?

kmarinas86

I figure that it is possible for temperature to decline in a fixed volume system that is thermally insulated. The reason why is that, from what I understand, is that random kinetic energy may have angular momentum. If we were to subject a volume of such energy to a rotating force (torque), then we should be able to de-randomize the rotational kinetic energy and induce a rotation of mass in that volume. That mass should have a lower barometric (static) pressure, but also it would have a higher dynamic pressure associated with the centripetal force on the gas (imposed by the forces which create the volume constraint). From what I understand, the P in PV=nRT applies only to BAROMETRIC or static pressure. Is this correct? Can an object really get colder doing neither "adiabatic work" nor dispersing thermal energy as heat to a colder reservoir? Or is this cooling effect exactly negated by the rotational work done on the system to induce the rotational alignment? Personally, I suspect that there is some mathematical argument which can show the latter to be wrong.

mfb

Where is the cooling effect? I think that your torque accelerates all particles (otherwise you get even more heating), or at least independent of their velocity. You just preserve the random movement in your gas and add a rotation to it.

Your perfectly isolated volume can have a net angular momentum, this degree of freedom does not account for temperature - even without any external torque.

kmarinas86

Couldn't entrainment of the gas with this added rotation be disproportionate in such a way that gas "aligns" with the rotation more so than it impedes, resulting in a net rotation greater than the input rotation?

If I understand correctly, this is not impossible. For example:
An example of a net rotation in excess of input torque is that of a bicycle wheel, which attempts to align the rotation of the wheel with the rotational work being attempted by input torque. If you have a bicycle treading forward, and if you apply a torque downward on the "starboard" side of the bicycle's C.O.G., the bicycle wheels themselves will attempt (due to gyroscopic precession) to pivot to the "starboard" side (independent of the "leaning of the bike"). If you are viewing this from the "starboard" side, further out, then you see both wheels rotating clockwise. This (clockwise) is the same direction as the torque viewed from the rear of the bicycle, as well as the same direction the wheels will appear to rotate from the (initial rear point of view) after the bike begins to veer to the right.
In other words, the precession is such that the spin of the wheel acts to align with the external torque. The result is that the spin of the wheel adds to the spin around the initial torque axis. If you keep the torque axis fixed with respect to an observer standing still on the pavement, and not rotating with the bicycle turn, then at some point, the bicycle wheel axis is aligned with the torque axis, ceasing the precession.
Also, if understand correctly, this would also explain the phenomenon of magnetic susceptibility seen with paramagnetic materials.

mfb

But this spin is already present.

Do you try to violate angular momentum conservation? If not, where is your point? If yes, please publish a paper about your completely new theory first and wait until it gets accepted by the scientific community ;).

kmarinas86

No I don't. If the angular momentum axis of the wheel is swung to align with the axis of applied torque, then the amount of angular momentum of the wheel around that axis increases by an amount greater than the time integral of the input torque. Therefore, to conserve angular momentum, there must be an external medium or internal medium having angular momentum axes which must swing toward the opposite direction so as to cancel that out.

Going back to the previous example (of the opening post), if we speak of causing a rotation of a gas in the clockwise direction in excess of that applied by a clockwise external torque, then one way of conserving angular momentum would be inducing sub-cells of the gas to undergo a sort of "retrograde" motion with respect to the overall rotation of the gas. That this "retrograde" motion is likely is implied by the fact that when a "Hot Wheels" toy car is made to travel through a loop in a clockwise direction with respect to an observer, the wheels of the "Hot Wheels" toy car must spin counter-clockwise to maintain traction with the track (i.e. limit sliding friction), or in other words, the vector spin angular momentum of the wheels has a sign opposite to its vector orbital angular momentum, and hence it has "retrograde" motion.

Another way of conserving the angular momentum would be to allow the gas to transfer some of its energy to the walls to move them in the opposite direction, though this would be far more unlikely as it would be far more stable for the gas and the walls to spin in the same direction to reduce to their sliding friction. That makes the first option, which utilizes an internal medium as a way conserve angular momentum, the more probable means where the total angular momentum of the system may be conserved.

DrDu

Why so complicated?
You can e.g. mix salt and ice isochorically and adiabatically.
Temperature will drop way below 0 C.

kmarinas86

I was thinking more along the lines of just a single substance (specifically, a gas) with neither phase changes nor chemical reactions.