pressure integral

The pressure integral (used in modeling stellar structure) relates a gas's pressure to particle momenta and density.

        ∞
P = 1/3 ∫ nppv dp
        0

• P - pressure.
• p - momentum.
• n_pdp - number of particles per unit volume with momentum p.
• v - velocity of the particle (with the given momentum).

(If the particles have a variety of masses, then velocity is not related to momentum and evaluation is less straightforward, but I believe you can do each type of particle separately and sum the results.) This form applies to any particles with momenta, and can be applied photons for light pressure as well as molecules.