Gay-Lussac's Law
Gay-Lussac's Law relates gas pressure and temperature at constant volume.
Learn the formula P₁/T₁ = P₂/T₂ with worked examples.
The Formula
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, gas molecules move faster and collide with container walls more forcefully, raising the pressure.
This law was formulated by French chemist Joseph Louis Gay-Lussac in 1808. It is one of the fundamental gas laws alongside Boyle's Law and Charles's Law. All temperatures must be expressed in Kelvin (K), not Celsius or Fahrenheit, for the formula to work correctly.
Variables
| Symbol | Meaning |
|---|---|
| P₁ | Initial pressure (in atm, Pa, or any consistent unit) |
| T₁ | Initial absolute temperature (in Kelvin) |
| P₂ | Final pressure (same unit as P₁) |
| T₂ | Final absolute temperature (in Kelvin) |
Example 1
A sealed container of gas is at 2.0 atm and 300 K. If the temperature is raised to 450 K, what is the new pressure?
Identify the values: P₁ = 2.0 atm, T₁ = 300 K, T₂ = 450 K
Apply the formula: P₂ = P₁ × (T₂ / T₁)
P₂ = 2.0 × (450 / 300) = 2.0 × 1.5
P₂ = 3.0 atm
Example 2
A tire has a pressure of 35 psi at 20°C (293 K). After driving, the temperature rises to 50°C (323 K). What is the new pressure?
Identify the values: P₁ = 35 psi, T₁ = 293 K, T₂ = 323 K
Apply the formula: P₂ = P₁ × (T₂ / T₁)
P₂ = 35 × (323 / 293) = 35 × 1.1024
P₂ ≈ 38.6 psi
When to Use It
Use Gay-Lussac's Law whenever you need to relate pressure and temperature changes in a sealed container.
- Predicting tire pressure changes with temperature fluctuations
- Calculating pressure inside sealed vessels when heated or cooled
- Understanding pressure cooker behavior
- Safety calculations for pressurized gas cylinders exposed to heat