# How does pressurized gas constantly push?

If a gas, such as hydrogen, is pressurized into an air tight container, a force in terms of pascals (or whatever unit you want to use) is exerted, correct? That is what pushes against every surface within the container. But what I don't understand is how the gas can constantly push against the walls without being supplied more energy. Does the force of pressure not need energy, or am I missing something? What about when the force is used to move something, such as in a hydraulics system?

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The gas isn't doing any work (expending energy) because it isn't moving the walls of the container. Each time a gas molecule hits the walls of the container it bounces off imparting a force on the container that balances out the force of the container on the gas. In this way the energy of the gas is conserved. The force in a hydraulic system does push the walls of the container and does a great deal of work. – Brandon Enright Jan 14 '14 at 5:13
Remember, $W = f \cdot \Delta d$ and when the walls aren't moving $\Delta d = 0$ and therefor no mater how much force $f$ is imparted on the walls, the work $W$ is $0$ too. In hydraulics the wall moves and $\Delta d > 0$ so work is done (energy is expended). – Brandon Enright Jan 14 '14 at 5:14
The collisions are elastic. – Ruben Jan 14 '14 at 6:25
@Ruben the collisions don't have to be elastic. As long as the gas in the container and the external environment are in thermal equilibrium the collisions can be inelastic and the energy flowing out of the container do to inelastic collisions will balance out the energy flowing into the container via inelastic collisions. – Brandon Enright Jan 14 '14 at 7:41
@BrandonEnright Yes, you are right. I did not know that before (the reason being that the education system tells you A this year, and then the next it tells you it is actually B). Thanks for pointing it out. – Ruben Jan 14 '14 at 12:22

The reason for why you do not need to supply any energy is because there is no net work done.

Lets assume for a second your container exists in a vacuum. This is essentially an isolated system, not considering black body radiation. This means that none of the energy contained in the box ever escapes and is doomed to stay in the box for all eternity.

If your container contains an ideal gas the pressure in the container is given by

$$P = \frac{Nk_bT}{V}$$

and as long as the container does not change it's volume this means that the temperature is the only thing that determines the pressure in the box.

Now the kinetic theory of gasses tells us that the temperature depends linearly on the average kinetic energy of the gas particles, and that all collisions are elastic. This means that the average kinetic energy stays the same, as do temperature, and hence also pressure.

Now in the real world my assumptions does not hold, per se, but they are a reasonable approximation given that the system is in thermal equilibrium with it's surroundings; That is the container receives as much heat energy as it looses per unit time.

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A force does not require a constant input of energy to exist. Energy is only required to perform work, which is exerting a force over a distance.

$$W = \mathbf F \centerdot \Delta \mathbf x$$

That distance is key. In your example, if the size of the container does not change, no energy is expended no matter how long the force lasts. If the force is used to move something, then work is expended. In the case of a piston, when the gas is compressed, work is done on the gas, and its internal energy rises. When the gas expands, the gas does work on the piston (and through it, whatever else is connected), and the internal energy of the piston is reduced.

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Let me add a note: A good example is always a simple table . The table must exert a constant force all the time to hold up a book lying on it. No energy is spent to do this. – Steeven Aug 29 '15 at 10:02

The real reason is that the gas and container are assumed to be in thermal equilibrium. If the container could radiate into void, then the pressure would slowly decline as the temperature fell. The ideal gas law ignores inter-molecular forces and the finite size of molecules, so eventually the gas will condense and other forces, other than elastic collisions, will come into play. A finite pressure is produced by all real gases/liquids/solids thanks to the zero point 'force', even at absolute zero.

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