For a gas, temperature and volume are directly
proportional. Keeping everything else constant,
as the temperature of a gas goes up, its volume
goes up. As the temperature of a gas goes
down, its volume goes down.
If you heat up a gas, it expands - the gas
particles move faster, and they take up more
space. Imagine a balloon, that expands when
gas particles bang against the sides. (by
expanding, that keeps the pressure constant).
The faster the gas particles move, the more
they will push on the sides of the balloon,
expanding it. If, on the other hand, you cool
the gas down - you put your balloon on ice
- that slows the particles of gas down, so
the balloon will contract.
Jacques Charles is credited with this Gas
Law relating temperature and volume, although
he didn’t publish it - he may have been
too busy taking rides in hot air balloons.
A colleague, Joseph Louis Gay-Lussac, published
it and very honorably gave Charles credit.
Charles’s Law says that for a given amount
of gas, at fixed pressure, volume and temperature
are directly proportional. V ∝ T You can
write this mathematically as V = kT
where V = volume,
T = temperature in Kelvin, and
k = is a proportionality constant.
We can rearrange this equation so it reads
V/T = k, or the ratio of volume to temperature
is a constant, k.
Very often, Charles’s law is used to
compare two situations, a “before” and
an “after.” In that case, you can say
V1 /T1= k, and V2/T2 = k, so you can write
Charles’s law as
V1 /T1= V2/T2. Let’s see an example.
A hot air balloon has a volume of 2,800 m3
at 99 C°. What is the volume if the air cools
to 80 C°?
We’ll write Charles’s Law in the “before
and after” form:
V1 /T1= V2/T2.
We substitute in what we know - remember to
convert temperatures 
to Kelvin: Kelvin = C° + 273.15.
T1= 372.15 Kelvin, T2 = 353.15 Kelvin
2,800 m3/ 372.15 K = V2/ 353.15 K
solve for V2 (multiply both sides 
by 353.15K)
(353.15 K) (2,800 m3)/ 372.15 K = V2
V2 = 2657 m3
Here’s another example: At 0 C°, a gas
occupies 22.4L. How hot must the gas be, in
Celsius, to reach a volume of 25.0 L?
V1 /T1= V2/T2.
Convert temperature to Kelvin: Kelvin = C°
+ 273.15.
T1 = 273.15 K
Substituting in what we know: 22.4L/273.15K
= 25.0L/T2
Solve for T2 (I like 
to “cross multiply”)
(22.4L) T2 = (273.15 K)(25.0L)
T2 = (273.15K) (25.0L)/22.4L
T2 = 304.9 K
Convert to C°: C° = Kelvin - 273.15
T2 = 31.7 C°
Charles’s law relates temperature and volume
for a gas, but there are other gas laws which
relate the other essential variables associated
with a gas. Boyle’s Law is the relationship
between pressure and volume.
Gay-Lussac’s Law is the relationship between
pressure and temperature. And the combined
gas law puts all 3 together: Temperature,
Pressure, and Volume. Notice that to use any
of these laws, the amount of gas must be constant.
Avogadro’s Law describes the relationship
between volume and the amount of a gas (usually
in terms of n, the number of moles). When
we combine all 4 laws, we get the Ideal Gas
Law. To decide which of these gas laws to
use when solving a problem, make a list of
what information you have, and what information
you need. If a variable doesn’t come up,
or is held constant in the problem, you don’t
need it in your equation.
