MadSci Network: Physics |
Dear Professor Hahn: Let's look at your question on a very basic level. Assume you have an open container, at room temperature and atmospheric pressure. You pump air into the chamber at a pressure up 10 atmospheres and seal it off. The chamber was initially at room temperature and pressure inside and outside equal. Pumping the air into the chamber takes energy; tne molecules are closer together and collide with each other much more frequesntly, to 10X as frequently as you stuff them into the chamber. If this is done rapidly, then the chamber walls will heat up because they are being bombarded with air molecules at higher and higher frequenccy, and these collisions impart energy to the walls and heat them. The kinetic energy of the molecules gained by the "stuffing" process has been converted to heat energy as the walls heat up. Note that the rate of heat conduction away from the walls by the air outside is much lower because the collision frequencies of the outside air with the walls is much lower, so therefore there is not equilibrium and the wall temperature rises. Now if you leave the chamber around for several hours it will cool down because the surrounding gas will gradually conduct away the heat and eventually the entire high-pressure chamber will be at room temperature as before BUT it is full of gas at 10 atmospheres pressure, which means that the kinetic energy expended stuffing the chamber is now sitting there with stored potential energy, of an amount somewhat less than the initial kinetic energy because some of that was converted to heat which has been conducted away by the external gases. (You never get something for nothing!) So now you have the room-temperature gas at high pressure stored in the chamber. Although the gas collision frequency with the inner walls is still higher than the outside, all is in thermal equilibrium but you have this "bomb" with high potential energy sitting there. Now you suddenly let the air out of the chamber. The collision frequency of molecules with the inside wall drops very rapidly. The potential energy of the molecules making 10X as many collisions/second is converted to kinetic energy of the gas stream leaving the chamber, with the consequence that the intercollision frequency goes down as the pressure drops and the gas cools below room temperature, since that is where it started before venting. With the body of gas moving at high velocity and expanding the temperature drops and heat is conducted from the chamber walls to the cooler gas whose presure is falling within the chamber and being exhausted. Potential energy is being "taken away from" the chamber. The gas does not really "absorb" energy; it has high potential energy which is converted into kinetic energy of high mass flow at reduced pressure during the exhausing phase. In principle if the heating of the gas during the initial compression were stored by maintaining the chamber at the temperature it rises to when pressurized, the approximate net effect of venting the chamber would essentially just reduce it to room temperature again. I hope this qualitative discussion has been of some help. R. Bersin....
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