Gay-Lussac’s Law: Pressure and temperature

Gay-Lussac’s Law (named after the 19th-century French scientist Joseph-Louis Gay-Lussac) deals with the relationship between the pressure and temperature of a gas if its volume and amount are held constant. Imagine, for example, that you have a metal tank of gas. The tank has a certain volume, and the gas inside has a certain pressure. If you heat the tank, you increase the kinetic energy of the gas particles. So they’re now moving much faster, and they’re hitting the inside walls of the tank not only more often but also with more force. The pressure has increased.

Gay-Lussac’s Law says that the pressure is directly proportional to the Kelvin temperature. Mathematically, Gay- Lussac’s Law looks like this:

P = kT (or P/T = k at constant volume and amount)

Consider a gas at a certain Kelvin temperature and pressure (T₁ and P₁), with the conditions being changed to a new temperature and pressure (T₂ and P₂):

P₁/T₁ = P₂/T₂

If you have a tank of gas at 800 torr pressure and a temperature of 250 Kelvin, and it’s heated to 400 Kelvin, what’s the new pressure? Starting with P₁/T₁ = P₂/T₂, multiply both sides by T₂ so you can solve for P₂:  [P₁T₂]/T₁ = P₂

Now substitute the values to calculate the following answer: P₂ = [(800 torr)(400 K)]/250 K = 1,280 torr This is a reasonable answer because if you heat the tank, the pressure should increase.

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