# Is pressure a force?

1. Sep 29, 2009

### Topher925

Very simple question but it has really been bothering me lately. Recently, a professor asked us this in class to which I said, "yes, of course it is" while everyone else said that it was not including the professor. He tried explaining it but I still don't understand.

We measure pressure by measuring a load created by a fluid, hence the units for pressure. However, for a pressure to exist a surface is not required. For example the pressure at the center of a balloon. Unless I'm mistaken, the pressure at the center of a balloon is the average force at which the gas particles interact with each other due to a change in their momentum from collisions. So practically the force would be better represented as the root mean square of all forces in all directions.

(from wikipedia)

Is this average force not equivalent to pressure, or do we have to define the molecular forces between molecules differently than pressure? In engineering we are taught to think of pressure as a load, but in chemistry we are taught to think of it as a state of matter. Which is it?

2. Sep 29, 2009

### Bob S

Hello Topher-
Pressure is measured in Pascals, or Newtons per square meter, or psi etc. It is force per unit area, If the pistons in my car are 10 cm diameter and the pressure after ignition is ~10 atm or 1 MPa, the downward force on the piston is about 7800 Newtons. So pressure is not a force. Pressure can create a force only on a surface.
Bob S

3. Sep 30, 2009

### diazona

You are mistaken on that, I believe. To reiterate Bob's point, pressure is a force per unit area. So the (average) pressure at the center of a balloon would be the average force per unit area with which the gas particles interact with each other due to changes in momentum from collisions.

There needs to be some sort of surface to have that area, of course, but it doesn't need to be a physical surface like the inside of a balloon. It could be an imaginary surface in space.

4. Sep 30, 2009

### tanujkush

See the units of the formula you have got, its got mass times velocity squared by length. That is (M*(L/T)^2)/L = M*L/T^2 - That is by definition a force not pressure. Pressure is force per unit area - Force/Area = (ML/T^2)/(L^2)=M/(LT^2)

Pressure is never the *same* thing as a load, although in common engineering language we often interchange the two words. Pressure is always distributed over an area (uniformly or otherwise).

In chemistry you are taught of pressure as a state variable because that is internal pressure meaning, the pressure that a gas would exert if say it was enclosed in a container. It is a state of the gas at that point because of Pascal's law that says the pressure inside a gas should be the same at all points at equilibrium. So pressure then becomes a macro-property for that gas and hence given the status of a state of the gas.

5. Sep 30, 2009

### Topher925

I'm not sure I agree with this. As I stated above you do not need a surface in order to create forces in a fluid. I'm well aware of what the units of pressure are, my question was if pressure is just an indirect way of quantifying the molecular forces of a fluid. Since we obviously can't directly measure forces created by fluid molecules we simply measure the average force over an area and call it pressure.

I think this is what I was missing. In order to take the average force from particle collision where there are no walls we have to assume some imaginary and arbitrary cross-section in space. From kinetic theory pressure is derived directly from the force of the fluid particles but instead of an average in all directions its just on a single wall. I guess it would be a little easier to say that pressure is the average molecular force per unit specific volume of a gas. Or in equation form:

$$P=\frac{\rho \nu^{2}_{rms}}{3}$$

I think I like that kgm-3m2s-2 much better than N/m2. It makes a lot more sense.

Last edited: Sep 30, 2009
6. Sep 30, 2009

### granpa

unless I am mistaken pressure is closer to potential energy than to force.

7. Sep 30, 2009

### Topher925

Potential energy? If anything it closer to kinetic.

8. Sep 30, 2009

### Bob S

The two relevant internal variables of a gas in equilibrium related to a force are:
1) Velocity distribution of molecules, which is dependent on temperature of the gas. This relates to the rms momentum impulse (momentum transfer) per molecule every time it scatters off another molecule or hits a surface.
2) Molecular density, which relates to the number of times per second a gas molecule collides with a specific surface area.
The product of these two relates to the force per unit area on a surface. However, the force, in and of itself, is not a relevant internal parameter of the gas.
Bob S

9. Oct 1, 2009

### fawk3s

i dont quite follow.. how can it be potential?

pressure is pretty close to force imo, but not quite.
in elementary physics its simply defined as "force per area unit." so i guess its "made" of force, but its not the force itself.

10. Oct 1, 2009

### Bob S

Internal variables of a gas include temperature and density. Remembering PV=nRT, these two variables are enough to determine pressure, but pressure should not be thought of as an internal variable in the sense that pressure (and force) are only relevant to , and only can be measured by, the force on a surface that is exposed to the gas on only one side. There is no net force on any arbitrary surface, physical or virtual, totally contained within the gas.
Bob S