What exactly is pressure?

Question

I can’t seem to wrap my head around the term pressure.

Vehicle tyres use air pressure, toilets faucets etc use pressure (presumably water pressure),
pressing onto something applies pressure, our blood has pressure, temperature is also affected by “pressure”.
I know there are various types of pressure, and I can’t think of any more examples at the moment, but my point is “pressure” sounds like a very arbitrary or vague umbrella term to me.

Help me make sense of it?

In: 3

Answer 1

So the pressure of inclosed gases are derived from the kinetic gas theory.

We model a gass closed into a container as a buch of balls with some velocity for each. We model it as an ideal gas which means that these little balls don’t interact with each other. (Or there are only elastic collisions between the balls, these are not quantitatively different. There are more realistic gas models that do consider interaction but it’s not a huge difference.)

Another thing about an ideal gas is that the velocity distribution over the particles are dependent on temperature. We’d expect a normal distribution (bell/Gauss curve) since very high/low velocities are unlikely. (This is the Maxwell-Boltzmann distribution.)

So we have some pretty solid average velocity for the tremendous amounts of particles. These particles collide with the walls of the container and exert a force. We can use conservation of energy/momentum to calculate the average force on the walls of the container. So we have some average force over some area so we norm for the the area to give us force over unit area, which is by definition what pressure is.

Of course as with many things in thermodynamics we make a bunch of approximations and take averages but since we usually consider a lot of particles, because of the law of large numbers, the deviations tend to cancel all together so averages fit reality really well. This microscopic model is pretty good, but for the aforementioned reasons macroscopic equations work accurately. These macroscopic equations relate pressure, volume, temperature, etc. These things. These are called equations of state, considering that a thermodinamical system is in equilibrium these quantities are related in some specific way. But of course all of these quantities come from the microscopic behaviour of particles, mostly their motion and mass.