Gay-Lussac's Law Calculator
Calculate the direct relationship between Pressure and Temperature ($P_1/T_1 = P_2/T_2$).
Initial State (1)
Final State (2)
Visualizing Relationship
The Physics of Pressure & Heat
Gay-Lussac's Law (also called Amontons's Law) describes the explosive relationship between heat and pressure. It explains everything from how car engines work to why you should never incinerate a battery.
Direct Proportionality
As Temperature goes UP, Pressure goes UP.
Kinetic Theory
Why does this happen? Temperature is essentially a measurement of speed.
- HeatAdding heat energy makes gas molecules fly faster.
- ImpactFaster molecules hit the container walls with more force and more frequently.
- ResultThis increased bombardment is what we measure as increased Pressure.
Rigid Containers
The condition "Constant Volume" is crucial. This law applies to things that cannot expand:
Pressure Cookers
By locking steam inside, the pressure rises significantly. This raises the boiling point of water to ~120°C, cooking food 4x faster.
Tire Safety
In winter, your low tire pressure light might come on. The air didn't leak out; it just got cold (T↓), causing the pressure to drop (P↓).
Gunpowder
When gunpowder ignites, it creates hot gas instantly. In the rigid barrel of a gun, the pressure spike is massive, forcing the bullet out at high speed.
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Frequently Asked Questions
What is Gay-Lussac's Law?
Gay-Lussac's Law states that the pressure of a given mass of gas is directly proportional to its absolute temperature, provided the volume remains constant. If you heat a rigid container of gas, the pressure rises.
What is the formula?
The mathematical expression is P1 / T1 = P2 / T2.
- P = Pressure (atm, kPa, mmHg)
- T = Temperature (Must be in Kelvin)
- Volume must be constant.
Why is it sometimes called Amontons's Law?
Guillaume Amontons discovered the relationship in the late 1600s, over a century before Joseph Gay-Lussac formally published it in 1802. Both names are correct, but Gay-Lussac is more common in modern textbooks.
Why must I use Kelvin?
Gas laws rely on Absolute Temperature. The Celsius scale has negative numbers and a zero point that doesn't mean 'zero energy'. Using 0°C in the denominator would start a division-by-zero error. Kelvin (K) starts at absolute zero, making the math work.
What volume is constant?
The law assumes a rigid container (like a steel scuba tank, a glass bulb, or a pressure cooker) that does not expand or contract significantly as potential pressure builds up.
What is a real-life example?
Pressure Cookers: The lid locks the volume. As the water boils and turns to steam, the temperature inside rises far above 100°C. This extreme heat increases the pressure effectively, forcing heat into food faster.
Why should I not throw spray cans in a fire?
Aerosol cans are rigid containers. If you heat them in a fire, the gas temperature soars. According to Gay-Lussac's Law, the pressure will also soar until it exceeds the metal's strength, causing a dangerous explosion.
Does this apply to car tires?
Yes! After driving for a while, friction heats up your tires. The air inside gets hot and the pressure increases. That's why you should measure tire pressure when they are 'cold' (before driving) to get an accurate reading.
What happens at Absolute Zero?
At 0 Kelvin (-273.15°C), molecular motion theoretically stops. Since pressure is caused by molecules hitting the walls, the pressure would drop to zero.
How is it different from Boyle's Law?
Boyle's Law relates Pressure and Volume (at constant Temp). Gay-Lussac's Law relates Pressure and Temperature (at constant Volume). One is inverse, the other is direct.
Why does popcorn pop?
It's Gay-Lussac's Law! The water inside the kernel turns to steam as it heats up. The hard shell acts as a rigid container. Eventually, the pressure becomes so great (P/T relationship) that the shell ruptures explosively.
What is Kinetic Molecular Theory?
It explains why the law works. Temperature measures the average kinetic energy. Higher T means faster particles. Faster particles hit the container walls harder and more often, resulting in higher Pressure.
Can I use Fahrenheit?
No. You must convert Fahrenheit to Rankine or Kelvin. Our calculator handles this conversion for you automatically.
Does this apply to liquids?
Generally, no. Liquids don't follow gas laws because their molecules are already packed closely together. Heating a liquid in a closed container can be even more dangerous (hydraulic rupture) due to thermal expansion.
What is the Combined Gas Law equivalent?
If you take the Combined Law (P1V1/T1 = P2V2/T2) and cross out the Volumes (since V1=V2), you are left with Gay-Lussac's Law.