For a gas, temperature and pressure are directly proportional. When you keep everything else
constant, as the temperature of a gas goes up, its pressure goes up. As the temperature
of a gas goes down, its pressure goes down.
If you heat up a gas, the gas particles move faster. If the gas is in a solid container,
with fixed volume, this means that the faster the gas particles move, the more times per
second they collide with the sides of the container. That registers as increased pressure.
The converse is also true - if you cool down this container of gas, that means the gas
particles are moving more slowly. So there will be fewer collisions with the sides of
the container per second, which means lower pressure.
Joseph Louis Gay-Lussac shares credit with Guillaume Amontons for establishing a Gas
Law describing the relationship between temperature and pressure. Gay-Lussac’s Law says that
when the volume and amount of gas is constant, pressure and temperature are directly proportional.
P ∝ T You can write this mathematically as P = kT
where P = pressure, T = temperature in Kelvin, and
k = is a proportionality constant. We can rearrange this equation so it reads
P/T = k, or the ratio of pressure to temperature is a constant, k.
Very often, Gay-Lussac’s law is used to compare two situations, a “before” and
an “after.” In that case, you can say P1 / T1= k, and P2 / T2 = k, so you can write
Gay-Lussac’s law as P1 / T1= P2 / T2. Let’s see an example.
Example 1: A canister of nitrogen gas has a pressure of 2000 psi (pounds per square
inch) at 20 C°. What will the pressure be if you increase the temperature to 25 C° ?
Let’s write down Gay-Lussac’s Law:
P1/ T1= P2 / T2, because we have a “before” and “after.”
Convert temperatures to Kelvin: Kelvin = C°+ 273.15.
T1 = 293.15 K, T2 = 298.15 K Substitute in what we know:
2000 psi / 293.15K = P2/ 298.15 K
Solve for P2 (multiply both sides by 298.15 K)
P2 = (2000 psi )(298.15 K)/293.15 K
P2 = 2034 psi
Example 2. Here’s another example: At 10 C°, a gas exerts 0.95 atm of pressure. At
what temperature (in Celsius) will it exert a pressure of 0.75 atm?
P1 /T1= P2/T2. Convert temperatures to Kelvin:
Kelvin = C°+ 273.15. T1 = 283.15 K
0.95 atm/ 283.15 K = 0.75 atm/T2 Solve for T2
T2 = (283.15 K)(0.75 atm)/0.95 atm T2 = 223.54 K
Convert to Celsius: 223.54K - 273.15 = - 49.6 C°
Gay-Lussac’s Law relates temperature and pressure for a gas, but there are other gas
laws which relate the other essential variables associated with a gas. Charles’s Law is
the relationship between temperature and volume. Boyle’s Law is the relationship between
pressure and volume. 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.