This simulation enacts the kinetic theory of gases - first proposed by Daniel Bernoulli in the 1730s, but not generally accepted until more than a century later.
He
suggested that gases are composed of countless millions
of tiny particles moving randomly through empty space (the velocity of each
gas molecule is shown with a blue arrow in the simulation), bouncing elastically
off each other and other objects. The pressure exerted by a gas is the sum
of the impact of these collisions (each shown with a red arrow). The smaller
the volume a given number of particles occupy, the greater the concentration
of collisions, and the higher the gas pressure.Bernoulli
conceived of heat, not as a separate entity,
but just as the motion of particles. So the higher the gas temperature, the
faster the molecules move, hitting objects more often and with a greater
impact, and thus exerting a higher pressure.This
simulation puts the kinetic theory of gases into
practice - albeit with just a few particles - allowing you to experiment
with a model of a gas in the same way you would a real one. But for Bernoulli
his theory was a conceptual model that could be used to work out formulae
predicting how such a gas would behave - an analytical rather than an
experimental approach. This predicted "ideal gas" behaviour could then be
compared to the behaviour of real gases.In
deriving the gas laws from Bernoulli's kinetic
gas model certain assumptions are made about the of the behaviour of the
molecules of this "perfect" or "ideal" gas; that the molecules are identical
tiny spheres occupying negligible volume, travelling in straight lines, with
no force exterted on them except in perfectly elastic collisions (no KE lost
or gained) with other molecules or the container walls.This
simulation departs from this ideal in that
the molecules have a significant size - allowing a reasonable rate of collisions
and exchange of kinetic energy between molecules. (Also, the speed distribution
resulting from this 2D simulation differs slightly from a more realistic
3D simulation.)Real
gases too depart from the ideal (in that
gas molecules occupy space and have some attraction to each other) but give
a good approximation to perfect gas behaviour at high temperature and low
pressure. The Van de Waals equation of state makes adjustments to the ideal
gas law to take account of the properties of "real" gas molecules -
giving better agreement with the behaviour of real gases at lower temperatures
and higher pressures.Kinetic gas theory links:
Kinetic gas theory: a brief intro
derivation1 derivation2 derivation3
Perfect gas assumptions and derivation
Early theories of gases
History of gas laws
Van de Waals equation of state1
Van de Waals equation of state2