# How can a small volume of gas balance the pressure exerted by the whole atmosphere?

Consider a balloon filled with Helium or even air for that matter. The membrane of the balloon is in equilibrium because the atmospheric pressure on it exerted by the atmosphere, the elastic force by the membrane and the outward pressure by the helium gas inside exactly balance.

My question is,how can such a small volume of gas inside the balloon balance the pressure exerted by the huge atmosphere? I think this has to do something with the fact that the pressure exerted by the atmosphere is due to its weight whereas the pressure exerted by the gas in the balloon is just due to its intrinsic tendency to expand.

Is this really the reason? If so, how can such a small amount of helium counteract the whole weight of the atmosphere? And are these two 'types' of pressures really different at the molecular level? Why?

It's because the atmosphere exerts a force in all directions. If you think of a thin layer of atmosphere surrounding the balloon, it also pushes against the atmosphere.

Of course the air in the balloon is also part of the atmosphere pushing outwards. You could just as easily have put a box on the table, and a lid on top. The air inside the box pushes from below and balances the pressure from above.

If you take the air out of the container (eg. condensing steam in a thin metal can), as you have probably seen, the atmosphere crushes it without problem. See "55 gallon steel drum can crush"

• But that still doesn't answer my question. I'm aware that the air in the balloon is a part of the atmosphere, but how can such a volume it exert the atmospheric pressure all by itself? – Gerard Jan 30 '15 at 13:53
• Gas pressure derives from the motion of molecules. Those in the balloon are no different form those in the surrounding atmosphere. The skin of the balloon is just a arbitrary surround, no different to soap bubble, in which the pressure on each side of the film is the same. – iantresman Jan 30 '15 at 13:56
• The forces balance. Pressure is force per unit area. The whole atmosphere is not pressing on the balloon. Just the part in contact with the balloon. And that is the same size as the balloon that presses back. – mmesser314 Jan 30 '15 at 14:11
• @gerard, the box example is absolutely relevant to your question. Ask yourself, "why, when I close an empty box, is the box not immediately crushed by the immense weight of the atmosphere?" The answer is, because before I closed the lid, the air in the box was part of the atmosphere. It was already compressed to the same pressure as the air outside the box. The pressure inside the box pushing out is exactly the same as the pressure outside pushing in. That means, no net pressure on the walls of the box. – Solomon Slow Oct 28 '15 at 2:43
• Only difference between the balloon and the box is that, in order to get the air/helium/whatever into the balloon, it has to be pumped up to an even higher pressure in order to inflate the elastic balloon. – Solomon Slow Oct 28 '15 at 2:47

All pressure$^1$ is due to a material wanting to expand.

Pressure is defined as a force over an area. In the case of a gas, the force isn't a constant but comes from the time and area average of many collisions with your measuring surface. You can increase the average force by either increasing the number of particles colliding each second by increasing the density$^2$, or you can increase how hard each particle hits by increasing their velocities by increasing the temperature. You can see this from a version of the ideal gas law:

$$P=\rho\,R^*\,T$$

Where $P$ is pressure, $\rho$ is the density, $T$ is the temperature (in absolute units)$^3$, and $R^*$ is the specific gas constant.

In the case of a balloon the temperature should be roughly equal on each side of the balloon and isn't much in our control$^4$. Thus to fill a balloon we must cram more and more molecules into the balloon so the density is high enough to balance the atmospheric pressure.

So then one may wonder how people can blow up a balloon with their lungs, if the weight of the atmosphere is creating the pressure on the outside of the balloon. The answer is that the atmosphere helps us out by compressing the outside of our lungs helping us push the air into the balloon.

$^1$ Dynamic pressure also includes pressure due to a change in velocity, like a wave pushing someone over. However, static pressures are all about the material trying to return to its most relaxed state. Sometimes, in the case of liquids and solids this can mean there's a negative pressure if the liquid or solid is being stretched.

$^2$ The number of collisions is also increased by increasing the velocity of each collision. This means that the velocity gets to contribute twice. Fortunately temperature is dependent on the average square velocity, so the pressure just depends linearly on temperature.

$^3$ The temperature must be in absolute units because the pressure would only be zero at absolute zero, not say the freezing point of water (Celsius), or a saltwater slushy (Fahrenheit).

$^4$ If you place the balloon in the freezer, its temperature will decrease, but the atmospheric pressure will still be pushing on the outside so the balloon will collapse until the pressure is balanced by the increased density.