Equation
The equation uses the following state variables: the pressure of the fluid p, total volume of the container containing the fluid V, number of moles n, and absolute temperature of the system T.
One form of the equation is
where
is the volume of the container shared between each particle (not the velocity of a particle),
is the total number of particles, and
is Boltzmann's constant, given by the universal gas constant R and Avogadro's constant NA.
Extra parameters are introduced: a is a measure for the attraction between the particles, and b is the average volume excluded from v by a particle.
The equation can be cast into the better known form
where
is a measure of the attraction between the particles,
is the volume excluded by a mole of particles.
A careful distinction must be drawn between the volume available to a particle and the volume of a particle. In particular, in the first equation v refers to the empty space available per particle. That is, v is the volume V of the container divided by the total number nNA of particles. The parameter b, on the other hand, is proportional to the proper volume of a single particle - the volume bounded by the atomic radius. This is the volume to be subtracted from v because of the space taken up by one particle. In Van der Waals' original derivation, given below, b is four times the proper volume of the particle. Observe further that the pressure p goes to infinity when the container is completely filled with particles so that there is no void space left for the particles to move. This occurs when V = nb.
Read more about this topic: Van Der Waals Equation
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