🔬 Gay-Lussac's Law Calculator
Calculate the relationship between pressure and temperature of an ideal gas at constant volume. Enter any three of the four variables (P₁, T₁, P₂, T₂) and the calculator will find the fourth using the formula P₁/T₁ = P₂/T₂. Temperatures must be in Kelvin for accurate results.
What Is Gay-Lussac's Law?
Gay-Lussac's Law (also known as the Pressure-Temperature Law) states that for a fixed amount of gas held at a constant volume, the pressure of the gas is directly proportional to its absolute temperature. The mathematical relationship is:
P₁ / T₁ = P₂ / T₂
where P₁ and T₁ are the initial pressure and temperature, and P₂ and T₂ are the final pressure and temperature.
This law was first published by the French chemist and physicist Joseph Louis Gay-Lussac in 1809. Together with Boyle's Law (pressure-volume) and Charles's Law (volume-temperature), it forms the three classical gas laws and is the constant-volume special case of the Ideal Gas Law (PV = nRT).
Key characteristics of Gay-Lussac's Law:
- Direct proportionality: As temperature increases, pressure increases proportionally.
- Constant volume: The gas must be in a rigid container with fixed volume.
- Absolute temperature: Temperature must be measured in Kelvin (K) , Celsius and Fahrenheit do not work because they are not absolute scales.
How to Use This Calculator
This calculator solves for any one of the four variables in Gay-Lussac's Law:
- P₁ , Initial pressure
- T₁ , Initial temperature (must be in Kelvin)
- P₂ , Final pressure
- T₂ , Final temperature (must be in Kelvin)
To use the calculator:
- Select which variable you want to solve for using the dropdown.
- Enter the three known values in the corresponding input fields.
- Press "Calculate" to find the missing value.
- The calculator will show the step-by-step solution and the final result.
For example, to find the final pressure when a gas at 1.0 atm and 300 K is heated to 600 K:
P₂ = P₁ × T₂ / T₁
P₂ = 1.0 × 600 / 300
P₂ = 2.0 atm
Real-World Applications
- Tire pressure changes: Tire pressure increases in summer and decreases in winter , about 1 psi per 10 °F temperature change.
- Pressure cookers: Sealed pressure cookers use this principle to raise the boiling point of water.
- Aerosol can warnings: "Do not store above 50 °C" , heating causes pressure to rise, which can burst the can.
- Gas cylinders: Pressure in sealed gas cylinders rises on hot days, which is why they have safety relief valves.
❓ Gay-Lussac's Law FAQ
What is Gay-Lussac's Law formula?
The formula is P₁/T₁ = P₂/T₂. It relates the initial and final pressures and temperatures of a gas at constant volume.
Why must temperature be in Kelvin?
Gay-Lussac's Law uses absolute temperature. Celsius and Fahrenheit are relative scales that start at arbitrary points, so they break the proportional relationship. Always convert to Kelvin using K = °C + 273.15.
What are the conditions for Gay-Lussac's Law?
The law applies when volume is constant and the amount of gas is fixed (constant number of moles).
Is Gay-Lussac's Law the same as Charles's Law?
No. Gay-Lussac's Law relates pressure and temperature at constant volume (P–T). Charles's Law relates volume and temperature at constant pressure (V–T).
What is the difference between gauge pressure and absolute pressure?
Gauge pressure is measured relative to atmospheric pressure. Absolute pressure includes atmospheric pressure. For gas law calculations, use absolute pressure (add atmospheric pressure to gauge readings).
How does tire pressure change with temperature?
For every 10 °F change in temperature, tire pressure changes by about 1 PSI. This is a direct application of Gay-Lussac's Law.
Can I use this calculator for real gases?
Gay-Lussac's Law is accurate for ideal gases at moderate pressures. Near liquefaction or at very high pressures, real-gas corrections are needed.
How accurate is this calculator?
This calculator uses the exact formula P₁/T₁ = P₂/T₂. Accuracy depends on the precision of the input values. You can adjust the decimal precision in the output.
Is this calculator free?
Yes, this calculator is completely free to use. No registration or personal data storage is required.
Who discovered Gay-Lussac's Law?
Gay-Lussac's Law was discovered by Joseph Louis Gay-Lussac (1778–1850), a French chemist and physicist, and published in 1809.