Gay–Lussac’s Law

Pressure of a confined gas increases with increasing temperature. If the temperature of the gas increases enough, the container can explode because of the pressure that builds up inside of it. The relationship between the pressure and temperature of a gas is described by Gay–Lussac’s law. ‘Gay–Lussac’s law states that the pressure of a sample of gas is directly proportional to the absolute temperature when volume remains constant’.

Gay–Lussac’s law can be expressed as follows.

where P is the pressure and T is the temperature of the gas.

For two different conditions 1 and 2, Gay–Lussac’s law can be expressed as

where T₁ and P₁ are absolute temperature and pressure, respectively, at condition 1 and T₂ and P₂ are absolute temperature and pressure, respectively, at condition 2.

Example 1.27: A cylinder of a gas has a pressure of 5 atm at 50°C. At what temperature in °C will it reach a pressure of 12 atm?

Solution:

Given: P₁ = 5 atm; T₁ =273 + 50 = 323 K; P₂ = 12 atm; T₂ = ?.