Gay-Lussac's Law Calculator

Solve for pressure or temperature at constant volume using P₁/T₁ = P₂/T₂. Leave one field blank.

⚠ Temperature seems very low for Kelvin. Did you forget to convert from °C?
Result:

Related Calculators

Most Popular

Ideal Gas Law

PV = nRT
Open Calculator →

Combined Gas Law

P₁V₁/T₁ = P₂V₂/T₂
Open Calculator →

Charles's Law

V₁/T₁ = V₂/T₂
Open Calculator →

Boyle's Law

P₁V₁ = P₂V₂
Open Calculator →

Dalton's Law

Pₜₒₜₐₗ = ΣPᵢ
Open Calculator →

Avogadro's Law

V₁/n₁ = V₂/n₂
Open Calculator →

Volume of Gas

V = nRT/P
Open Calculator →

What is Gay-Lussac's Law?

Gay-Lussac's Law, also known as the Pressure-Temperature Law, states that the pressure of a gas is directly proportional to its absolute temperature when the volume is held constant. It was formulated by Joseph Louis Gay-Lussac in the early 1800s.

P₁ / T₁ = P₂ / T₂

Formula — Rearranged Forms

P₂ = P₁T₂ / T₁
T₂ = P₂T₁ / P₁
P₁ = P₂T₁ / T₂
T₁ = P₁T₂ / P₂

Step-by-Step Examples

Example 1: Find P₂ (gas is heated in a rigid container)

Given: P₁ = 1.5 atm, T₁ = 300 K, T₂ = 450 K. Find P₂.

1. Formula: P₂ = P₁T₂ / T₁
2. Substitute: P₂ = (1.5)(450) / 300
3. Calculate: P₂ = 675 / 300 = 2.25 atm

Example 2: Find T₂ (pressure drops)

Given: P₁ = 3.0 atm, T₁ = 400 K, P₂ = 1.5 atm. Find T₂.

1. Formula: T₂ = P₂T₁ / P₁
2. Substitute: T₂ = (1.5)(400) / 3.0
3. Calculate: T₂ = 600 / 3.0 = 200 K

Real-World Applications

  • Pressure cookers: Heating food in a sealed container increases internal pressure, cooking food faster.
  • Car tires in summer: Higher road temperatures increase tire pressure.
  • Aerosol cans: Warning labels say "Do not expose to heat" because increased temperature raises internal pressure, risking explosion.

Frequently Asked Questions

  • Gay-Lussac's Law states that the pressure of a gas is directly proportional to its absolute temperature when volume is held constant. As temperature increases, pressure increases proportionally. The formula is P₁/T₁ = P₂/T₂.

  • P₁/T₁ = P₂/T₂. Rearranged: P₂ = P₁T₂/T₁, T₂ = P₂T₁/P₁.

  • Use it when the volume of a gas is constant and you need to find how pressure or temperature changes. Common examples: pressure cookers, aerosol cans, car tires heating up.