# What happens to energy as air fills a vacuum?

by MrBi11
Tags: air, heat, ideal gas law, joules, vacuum
 P: 9 A cylinder with a piston to seal it starts empty. The are of the piston give a force of about 100 pounds. Lift the piston till there is 100 liters of vacuum. Now 2 cases: 1) release the piston, it slams down almost instantly. Since 1 atmosphere is about 10 newtons per centimeter, and 1 liter is 10 centimeter liters, 1 atmosphere-liter is 100 newton meters or joules. 100 liters makes for 10,000 joules of energy, as it hits the bottom. So loud bang, lots of heat. 2) Here is the real question. What happens if instead a hole is opened in the piston, letting air rush in. Ideal gas law says if volume increase/decreases work happens, but opening volume to connect, should create no work. In fact, opening a compressed bottle of air it cools of, as far as that air goes, it is expanding against a wall of other gas. Not precise i know. Either way, the atmosphere is lifted 100 liters, then dropped. Do that with a giant can of sand, drop it, bang. Open it, sand trickles down. Energy does not go the same place. Initially, the air expanding to fill the vacuum should cool slightly, then more air from outside the room, 100 liters of it, comes in to the room to equalize pressure. So, where does the 10,000 newtons go? Does the air in the room gain 10,000 joules of heat? or is the 10,000 joules distributed through the atmosphere, as would happen with the sand example?
 PF Patron Sci Advisor Thanks Emeritus P: 38,412 In all cases the energy goes into increased heat. Whether that happens slowly or quickly is not relevant.
 P: 9 With the closed piston, the "heat" hits the floor, and so is concentrated. with opening the cylinder, the floor clearly does not get heated up. The question is, is the heat concentrated in the room, or distributed among all the air moved, including outside the room?
P: 9

## What happens to energy as air fills a vacuum?

during expansion, the atmosphere is lifted, not heated. Just like lifting a hundred pound weight.

That lift is distributed however imperceptibly all the way to the very fuzzy top of the fluid.
In the first case, pressure remains uniform as the atmosphere falls.

In the second case, a low pressure wave propagates outward indefinitely, as far away as you can detect the "pop" of opening the vacuum. Is that where the heat goes?

Any experiments like this out there?
Mentor
P: 21,655
Welcome to PF!
 Quote by MrBi11 A cylinder with a piston to seal it starts empty. The are of the piston give a force of about 100 pounds. Lift the piston till there is 100 liters of vacuum.
You should be more precise and consistent with your units: it is pretty hard to follow your post.

Regardless of whether you really mean pounds or Newtons, 100 L (0.1 cubic meter) of vacuum (at sea level) is all you need to know for the energy. For simplicity, we'll say we have a .1 square meter column, 1m high. The force is 1010 N and the potential energy is 10,100 J.
 2) Here is the real question. What happens if instead a hole is opened in the piston, letting air rush in. Ideal gas law says if volume increase/decreases work happens, but opening volume to connect, should create no work. In fact, opening a compressed bottle of air it cools of, as far as that air goes, it is expanding against a wall of other gas. Not precise i know.
More complicated, but Conservation of Energy tells us it has to work out the same. The correct way to approach any thermodynamics problem is to assume conservation of energy holds and then look for the energy. So if the gas cools as it enters, what else happens to it that could affect the energy released? It is actually up to you, since you didn't specify an important issue: is the container insulated?
 Initially, the air expanding to fill the vacuum should cool slightly, then more air from outside the room, 100 liters of it, comes in to the room to equalize pressure.
Yes! So cooler means less energy, but more mass/denser means more energy, right?
 Do that with a giant can of sand, drop it, bang. Open it, sand trickles down. Energy does not go the same place.
What do you mean? Where do you think the energy goes?
 P: 9 What do i mean by energy does not go the same place? Drop a mile high can of sand, it all stays in contact, entire force is transmitted to the bottom as it hits. Energy concentrated at the bottom. Force on the ground initially the weight plus the force due to momentum. Really big bang. Open a hole in the bottom of a mile high can of sand, the sand on the bottom falls first, and that fall travels up the can. Energy of the fall of the top grain of sand impacts on where it lands, at the top of the pile. Energy distributed. Force on the ground builds gradually to reach the total weight. Force on ground never exceeds total weight by much. No big bang. So my question regarding air, is energy distributed in an analogous manner to filling grains of sand? Or is there some mechanism i'm overlooking that would concentrate heat at the location of the vacuum? Having worked with pressurized air, i can say if you allow air to enter a lower pressure container, it does not appear to heat up, but is that because it cooled off first, then heated up as pressure equalized? I am not sure, and can find no formulas covering this type of air movement. Unlike the ideal gas law implies, air does act somewhat as a container of sorts for itself. so one more times, not asking how much energy or if it ends up as heat. Where does the heat end up after air is done moving? Like the mile high sand can, pressure on the "floor" of the vacuum chamber never exceeds atmospheric pressure, and builds "slowly" if you consider the speed of sound slow.
P: 1,115
 Open a hole in the bottom of a mile high can of sand, the sand on the bottom falls first, and that fall travels up the can. Energy of the fall of the top grain of sand impacts on where it lands, at the top of the pile. Energy distributed. Force on the ground builds gradually to reach the total weight. Force on ground never exceeds total weight by much. No big bang
I am not sure what you are saying here. Potential energy of the sand is the same from the start, regardless of whether you drop it all at once or drop it grain by grain. And also, the kinetic energy of each grain of sand when it reaches the ground is the same whether all grains are dropped at once or one by one. The impulse upon hitting the ground is also the same in both cases. The difference is that all the tiny little forces of each grain of sand add up at once to give the larger force and the bang when dropped all at once.

By the way, the gas ( air ) that has entered the container will heat up and have a higher temperature in your hole experiment. That increase in temperature has an equivalent to the loud bang energy. Just thought I would mention that for you to ponder the question, "why does that happen."
 P: 339 Heat is just the random movement of molecules. Air molecules above the piston are colliding with it and thereby pushing it down. When you lift it against the force of the air you are accelerating air molecules. Imagine a ball bouncing of a wall. If the wall moves toward the ball it will accelerate the ball and give it more kinetic energy. So when you lift the piston you are giving the air molecules more energy and that means the air gets warmer. When the air pushes the piston down that process is reversed. The molecules slow down after the collision and therefore some of the heat of the air is transformed into kinetic energy of the piston. If the piston suddenly disappears air molecules will move into the cylinder. The average kinetic energy of the molecules will not change since they do not collide with a moving object, only with the stationary cylinder walls. While the air rushes into the cylinder their movement will not be completely random anymore but partly ordered. So one could say part of the heat energy of the air got transformed into energy of motion. However that does not mean that the kinetic energy of the molecules changed. It just means that ordered motion doesn't count as heat. After the cylinder has filled with air the motion of the molecules will be completely random again and the temperature of the air will be the same as it was before the piston disappeared. So in short, you didn't loose or gained any energy here. The amount of energy in the system is the same before and after the experiment. Heat energy just got turned into motion temporarily and then immediatly back into heat.
 HW Helper P: 6,772 There is a difference depending if the air performs work on an external object, such as the piston, or if the air experiences free expansion, without performing any work on an external object. Wiki article: http://en.wikipedia.org/wiki/Joule-Thomson_effect
P: 1,115
 Quote by rcgldr There is a difference depending if the air performs work on an external object, such as the piston, or if the air experiences free expansion, without performing any work on an external object. Wiki article: http://en.wikipedia.org/wiki/Joule-Thomson_effect
That describes is a constant enthalpy process, where the gas does an expansion.

This scenario of this post is not an expansion, but the filling up of a container with gas to an equal pressure as outside the container. Enthalpy of gas when outside container = Internal energy of gas when inside container.

See
http://web.mit.edu/16.unified/www/SP...es/node16.html