Effectively, this equation tells us that temperature, T, is directly proportional to volume, V, and
pressure, P. In metric units, volume is measured in m^3 , where 1m^3 = 10^6 cm^2.
The n stands for the number of moles of gas molecules. One mole (mol) is just a big number—
to be precise—that, conveniently, is the number of hydrogen atoms in a gram ofhydrogen. Because we deal with a huge number of gas molecules at any given time, it is usually a
lot easier to count them in moles rather than counting them individually.
The R in the law is a constant of proportionality called the universal gas constant, set at 8.31
J/mol · K. This constant effectively relates temperature to kinetic energy. If we think of RT as the
kinetic energy of an average molecule, then nRT is the total kinetic energy of all the gas molecules
put together.
Deriving the Ideal Gas Law
Imagine a gas in a cylinder of base A, with one moving wall. The pressure of the gas exerts a force
of F = PA on the moving wall of the cylinder. This force is sufficient to move the cylinder’s wall
back a distance L, meaning that the volume of the cylinder increases by = AL. In terms of A,
this equation reads A = /L. If we now substitute in /L for A in the equation F = PA, we get
F = P /L, or
If you recall in the chapter on work, energy, and power, we defined work as force multiplied by
displacement. By pushing the movable wall of the container a distance L by exerting a force F, the
gas molecules have done an amount of work equal to FL, which in turn is equal to P.
The work done by a gas signifies a change in energy: as the gas increases in energy, it does a
certain amount of work on the cylinder. If a change in the value of PV signifies a change in energy,
then PV itself should signify the total energy of the gas. In other words, both PV and nRT are
expressions for the total kinetic energy of the molecules of a gas.
Boyle’s Law and Charles’s Law
SAT II Physics will not expect you to plug a series of numbers into the ideal gas law equation. The
value of n is usually constant, and the value of R is always constant. In most problems, either T, P,
or V will also be held constant, so that you will only need to consider how changes in one of those
values affects another of those values. There are a couple of simplifications of the ideal gas law