Does pressure change with container shape?

My guess is no, but I could be wrong. If the surface area stays the same, I would think the pressure would stay the same.

If the shape changes from a sphere to a cube the surface area WILL INCREASE. If the volume remains the same (say from a 1 litre sphere to a 1 litre cube) how does this affect the internal pressure?

Pressure is defined as force per area.

If the area increases and the force applied remains the same, the pressure will decrease. If the area decreases andthe force applied remains the same, the pressure will increase.

You've emphasized VOL, while pressure is dependent on AREA.

The reason I mention volume is as a reference to the quantity of gas in the container.

Say there is a spherical container with a tap into it. The container has air in. The pressure inside the (self-supporting) container is equal to the pressure outside. Suddenly the shape of the container changes to a cube.

If, as you say, the answer to the question is simply that pressure is force divided by area and that if the area increases the pressure falls the container will 'suck' in more air from it's surroundings if the tap is opened.

What if the tap is then closed and the shape changes again to one with even greater surface area? Are you suggesting the container will take in even more gas?

If the tap is open the container will only 'suck' in air if the pressure inside the container is less than the pressure outside the container. If the pressure in the container is greater than outside, air will be sucked out of the container.

Your original question was answered by Miller.

Let me try it this way. As Miller says, if the force stays the same the only way to change the pressure is to change surface area.

The force is being provided by the gas bouncing off the inside walls. If the amount (and temperature) of gas stays the same (ie the volume) the force stays the same.

So far, so good.

The bit I am having difficulty with is the idea that the pressure inside will change (lessen) if a shape change provides more surface area. To take it to extremes from a sphere with a perfect inner surface (with the lowest surface area to volume ratio possible) to a multi-folded shape (with a high surface area to volume ratio).

I am only considering a change of internal shape in all of this.

How can the gas pressure change in a fixed volume of gas simply by changing the shape of the container it is in?

From the bit of pchem I remember, pressure is related to volume, not area: P1V1 = P2V2, etc. Therefore, at constant temperature, the pressure of a known quantity of gas will only change if the volume of its container changes. Surface area of the container shouldn't have any effect apart from its relationship to container volume.

However you change the shape if the volume remains the same so will the pressue. Assume the volume stays the same; as there is the same amount of gas, the density of the gas particles stays the same. This means at the surface, what ever the surface area, the density of particles remains the same, as pressure is caused by these particles hitting the surface the pressure WILL stay the same.

Think about this in terms of the converse situation: you have a sealed paper bag full of air. By pressing on the sides of the bag, you can change the volume but not the surface area of the bag. The pressure increases, the bag ruptures. If pressure was dependent on surface area rather than volume, a hydraulic jack wouldn't work.

Thanks for the responses. I like the density of gas particles explanation. I need to think more about it along those lines, especially the bit where, despite recognising the density of particles issue, there is more area over which those particles are acting (so to my mind reducing the pressure on the wall). Perhaps there is a balance between (1) the particle collisions with the wall being spread over a greater area and (2) the number of collisions possible as a result of the greater area available.

Uh Oh, I feel the need for some maths creeping in.

Maybe particles hitting the wall isn't the best way to think about it. What we're really talking about when we talk about pressure is the density of kinetic energy in a system. Think about the particles as packets of energy instead: when a number of these packets occupies a certain volume, there is a certain overall concentration of energy in the system, and so a certain amount of energy acting against the walls of the container. That's pressure. If you increase the volume of the container, the density of kinetic energy (the pressure) decreases. If you increase the energy of the packets (that is, you increase the temperature), the density of kinetic energy in the system increases again. Hence the dependence of pressure on temperature and volume.

Or maybe that doesn't help you. We all think about things a little differently...

Worked for me, pd. A sphere is the most efficient shape for containing pressure. The same fluid will always be under less pressure in a sphere than any other shape. The paper bag is a good example.

Yes there is more area for the particles to collide with but you will get the same number of collisions per unit area.

Think of a cake with raisans if you cut across the cake however you do it you will still get the smae number of raisans per unit area

Mutegi, the pressure of a given quantity of gas is determined by its volume and temperature. Changing the shape and surface area of the vessel will not change the pressure as long as the volume and temperature remain constant.

What does change is the amount of force the gas exerts on the vessel walls. Force equals pressure times area (Pressure x Area = lbs/square inch x square inches = lbs = Force), so compressed gas is usually stored in long cylinders rather than spheres since the total force exerted by the gas increases with the square of the radius. Excessive force induces stress in the container walls which could cause it to rupture.

The Cake! I get it now!

I've been wondering about this for years. Thanks very much for all the attempts at nailing it down.

Now, about those pesky gluons.........

Only kidding :wink:

Thanks again