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In most textbooks and thermodynamic lectures, the pressure is defined as the force on the walls of containers due to the incassecant beating of gas molecules divided by the area of the wall. Now, suppose I take a random point inside the container, what would be it's pressure at equilibrium and also non equilibrium conditions?

I am confused on the point whether we should have a wall or not to define pressure like is pressure a quantity defined 'over' the boundary of the container and undefined inside and outside? This seemed strange, to resolve, I thought of taking some random surfaces inside the container (say maybe a imaginary sphere) and then computing the pressure.

If the gas is in equilibrium,

$$ P \overline{V} = RT$$

and, if we calculate temperature from the temp of gas (all points have same because equilibrium) then we find pressure same for all points inside a gas. However this still is weird because how can you talk of 'pressure' without having a physical membrane which is being hit upon.

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Many physical quantities are defined in terms of "what would happen if ..." For example we might define the electric field strength at a point as the force per unit charge that acts on a small 'test' charge placed at the point, but we consider the electric field still to exist at the point, even if we don't have a test charge there.

It's similar with pressure. We consider a small surface to be placed at the point in question, even if that point is somewhere in the middle of the gas. We define the pressure as the force per unit area acting normally to that surface. We can measure the pressure with a sensor, and we can compute the pressure theoretically from the molecular impacts on an imaginary surface. But we still talk about the pressure at that point even if we don't have the surface there. It's the way we use the word.

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  • $\begingroup$ "we can measure pressure with a 'sensor'" .. what is this device called? $\endgroup$
    – Buraian
    Sep 5 '20 at 8:57
  • $\begingroup$ A pressure sensor! You can buy the sensor itself presented in chip-like packaging and requiring external circuitry and a display, and I expect you can buy a made-up instrument. $\endgroup$ Sep 5 '20 at 9:02
  • $\begingroup$ Interesting , not knowing of experimental methods has been hindering my learning haha $\endgroup$
    – Buraian
    Sep 5 '20 at 9:05
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    $\begingroup$ @PhilipWood Doesn't the type of pressure sensor you are referring to measure gauge pressure? I believe absolute pressure sensors involve a sealed high vacuum reference. $\endgroup$
    – Bob D
    Sep 5 '20 at 12:42
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    $\begingroup$ I last used a pressure sensing 'chip' about thirty years ago, and I'm afraid I forget the details. It was used to measure gas pressures both above and below atmospheric. $\endgroup$ Sep 5 '20 at 12:55

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