## Charles's Law for an Ideal Gas

Macroscopically, at a constant pressure
$p$
, the volume of a gas is proportional to its temperature
$T$
in Kelvins. We can write this relationship as
$V=kT$
or
$\frac{V}{T}=k$
where
$k$
is a constant. Microscopically, we can say
• If the temperature of a gas increases, the molecules of the gas have more kinetic energy (
$kinetic \: energy_{average} = \frac{3}{2}kT$
) and move faster (because
$kinetic \: energy=\frac{1}{2}mv^2$
).
• Faster moving molecules will have a larger change in momentum when they hit the walls of the container, and will hit the walls of the container more often, since they cover the distance between the walls in a shorter time.
• Force is equal to change in momentum each second, so grater change in momentum means a greater force.
• The volume of the gas increases then the rate of collision per unit area of the gas molecules with the walls of the container will decrease.
• The volume will increase until equilibrium is re established. This will happen when the volume of the container has increased in the same proportion as the temperature in Kelvin