Gay-Lussac's Law Calculator

Gay-Lussac's law: at constant volume, pressure is directly proportional to absolute temperature. Double temperature = double pressure. Used in pressure cookers, tire pressure, and gas cylinders.

💨 Gas Laws📐 P₁/T₁ = P₂/T₂🌡️ Constant Volume
P₁ (atm)
T₁ (K)
T₂ (K)
Please enter valid values.

Formula & Reference

VariableSymbolFormulaUnits
Gay-Lussac—P1/T1 = P2/T2—
Final PP2P1×T2/T1atm
Final TT2T1×P2/P1K
Always useTKelvin = °C + 273.15K

Step-by-Step Examples

Example 1
Heated Cylinder

Gas cylinder at 1.50 atm, 300 K is heated to 400 K.

  • P₂ = 1.50×400/300 = 2.00 atm
✓ 2.00 atm — pressure increases with temperature
Example 2
Pressure Cooker

Pressure cooker at 1.00 atm, 373 K (100°C). Heated to 121°C (394 K).

  • P₂ = 1.00×394/373 = 1.056 atm = 1.056 bar
✓ Pressure rises to 1.056 atm inside
Example 3
Tire Pressure

Car tire at 32 psi, 20°C (293 K). After driving: 50°C (323 K).

  • P₂ = 32×323/293 = 35.3 psi
✓ Tire pressure rises to 35.3 psi when hot

Real-World Applications

🚗
Tire Pressure
Tire pressure increases when driving because friction heats air inside tires (constant volume).
🍳
Pressure Cooker
Sealed cooker heats steam above 100°C under increased pressure.
🛢️
Gas Cylinders
Cylinder pressure must be checked at known temperature to calculate actual gas amount.
🚀
Rockets
Combustion gases at very high temperature produce enormous pressures in combustion chambers.

Common Mistakes to Avoid

⚠️
Kelvin not Celsius

T₁ and T₂ MUST be in Kelvin. Absolute temperature only. 25°C = 298 K.

⚠️
Constant volume required

P₁/T₁ = P₂/T₂ only at constant volume. If volume changes, use combined gas law.

⚠️
Same pressure units

P₁ and P₂ must use identical units: both atm, both Pa, both psi, etc.

Frequently Asked Questions

When was Gay-Lussac's Law discovered? ▾
Joseph Louis Gay-Lussac published this relationship in 1809, based on Jacques Charles's earlier unpublished work (1787).
Why does pressure rise when temperature rises? ▾
Higher temperature = higher molecular speed = harder collisions with container walls. Harder collisions = more force per area = higher pressure.
How does this apply to autoclave sterilization? ▾
Steam autoclave: sealed chamber heated to 121°C. Pressure rises to 1.058 atm. High temperature and pressure sterilize medical equipment.
What happens to gas at very high temperature? ▾
At high enough temperatures, gas molecules gain enough energy to dissociate or ionize. This is plasma physics, beyond ideal gas behavior.
Is Gay-Lussac's Law related to the third gas law? ▾
Yes. Combined Gas Law = P₁V₁/T₁ = P₂V₂/T₂ combines Boyle (V1/V2 = P2/P1 at const T), Charles (V1/V2 = T1/T2 at const P), and Gay-Lussac (P1/P2 = T1/T2 at const V).

Related Chemistry Calculators

💨 Boyle Law💨 Charles Law💨 Combined Gas Law⚗️ Ideal Gas Law💨 Dalton Law

Formula Explorer connections

Interpretation: This relationship converts chemical amount, mass, composition or balanced-equation ratios into a reaction quantity. Assumption: Use a balanced reaction, consistent units and the correct molar mass. Purity, side reactions and limiting reagents can change experimental results.

Grams to Moles Calculator →Limiting Reagent Calculator →Mass Percent Calculator →Chemistry Formula Explorer →