Editing Pressure (section)

===Formula===
{{Conjugate variables (thermodynamics)}}
[[File:Pressure force area.svg|200px|right]]
Mathematically:<ref name="Georgia State University, Physics & Astronomy">{{cite web |url=http://hyperphysics.phy-astr.gsu.edu/hbase/press.html |title=Pressure |author=R Nave |website=Hyperphysics |publisher=Georgia State University, Dept. of Physics and Astronomy |access-date=2022-03-05 }}</ref>
<math display="block">p = \frac{F}{A},</math>
where:
*<math>p</math> is the pressure,
*<math>F</math> is the magnitude of the [[normal force]],
*<math>A</math> is the area of the surface on contact.

Pressure is a [[Scalar (physics)|scalar]] quantity. It relates the [[vector area]] element (a vector normal to the surface) with the [[normal force]] acting on it. The pressure is the scalar [[proportionality constant]] that relates these two normal vectors:
<math display="block">d\mathbf{F}_n = -p\,d\mathbf{A} = -p\,\mathbf{n}\,dA.</math>

The minus sign comes from the convention that the force is considered towards the surface element, while the normal vector points outward. The equation has meaning in that, for any surface ''S'' in contact with the fluid, the total force exerted by the fluid on that surface is the [[surface integral]] over ''S'' of the right-hand side of the above equation.

It is incorrect (although rather usual) to say "the pressure is directed in such or such direction". The pressure, as a scalar, has no direction. The force given by the previous relationship to the quantity has a direction, but the pressure does not. If we change the orientation of the surface element, the direction of the normal force changes accordingly, but the pressure remains the same.{{citation needed|date=October 2021}}

Pressure is distributed to solid boundaries or across arbitrary sections of fluid ''normal to'' these boundaries or sections at every point. It is a fundamental parameter in [[thermodynamics]], and it is [[conjugate variables (thermodynamics)|conjugate]] to [[Volume (thermodynamics)|volume]].<ref>{{cite journal |last1=Alberty |first1=Robert A. |title=USE OF LEGENDRE TRANSFORMS IN CHEMICAL THERMODYNAMICS (IUPAC Technical Report) |journal=Pure Appl. Chem. |date=2001 |volume=73 |issue=8 |pages=1349–1380 |doi=10.1351/pac200173081349 |s2cid=98264934 |url=http://publications.iupac.org/pac/2001/pdf/7308x1349.pdf |access-date=1 November 2021 |quote=See Table 1 Conjugate pairs of variables ... (p.1357)}}</ref> It is defined as a [[derivative]] of the [[internal energy]] of a system:<ref>{{cite book |last1=Salinas |first1=Silvio R. A. |title=Introduction to statistical physics |date=2001 |publisher=Springer |location=New York |isbn=0-387-95119-9 |page=42}}</ref>
:<math display="block">p = -\left(\frac{\partial U}{\partial V}\right)_{S, N},</math>
where:
*<math>U</math> is the internal energy,
*<math>V</math> is the volume of the system,
*The subscripts mean that the derivative is taken at fixed [[entropy]] (<math>S</math>) and [[particle number]] (<math>N</math>).