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Pressure and kinetic energy

The pressure exerted by the collisions of the N {\displaystyle N} gas particles with the surface can then be found by adding the force contribution of every particle and dividing by the interior surface area of the volume, P = N F ¯ A = N L F V {\displaystyle P={\frac {N{\overline {F}}}{A}}={\frac {NLF}{V}}} ⇒ P V = N L F = N 3 m v 2. {\displaystyle \Rightarrow PV=NLF={\frac {N}{3}}mv^{2}.}