Gay-Lussac's Law states that pressure and temperature are directly proportional at constant volume. Heat a gas in a fixed container and its pressure increases proportionally.
P₁ / T₁ = P₂ / T₂
Initial pressure / initial temperature = Final pressure / final temperature
ALWAYS convert °C or °F to Kelvin before using Gay-Lussac's Law. Using Celsius will give completely wrong answers!
K = °C + 273.15
Example: 25°C = 298.15 K (often rounded to 298 K)
P ∝ T (at constant V and n)
Common Units: atm, mmHg, torr, kPa, Pa, bar, psi
Pressure before the temperature change
Units: K (Kelvin) - MUST USE KELVIN!
Temperature before the change
❌ Do NOT use °C or °F directly!
Units: Same as P₁
Pressure after the temperature change
Units: K (Kelvin) - MUST USE KELVIN!
Temperature after the change
Volume (V) must remain constant
Amount of gas (n) must remain constant
Container must be rigid (cannot expand)
P₂ = P₁T₂ / T₁
Most common use!
T₂ = P₂T₁ / P₁
P₁ = P₂T₁ / T₂
T₁ = P₁T₂ / P₂
T₁ = 25 + 273 = 298 K
T₂ = 100 + 273 = 373 K
P₁/T₁ = P₂/T₂
P₂ = P₁T₂ / T₁
P₂ = (2.50 atm)(373 K) / (298 K)
P₂ = 932.5 atm·K / 298 K = 3.13 atm
Answer: P₂ = 3.13 atm
✅ Makes sense: Temperature increased by 25%, pressure increased by 25%
Drive on hot pavement → tire heats up → pressure increases → check tire pressure when cool!
Heat sealed pot → temperature rises → pressure builds up → cooks food faster at higher pressure
Warning: "Do not heat" - hot can = high pressure = explosion risk!
Autoclave sterilization: high temperature creates high pressure to kill microorganisms
THE #1 MISTAKE! Temperature MUST be in Kelvin. Using °C gives completely wrong answers. Always convert: K = °C + 273.
Gay-Lussac's Law ONLY works when volume is constant (rigid container). If V changes, use the Combined Gas Law instead.
P₁ and P₂ must be in the same units. T₁ and T₂ must BOTH be in Kelvin. Convert before calculating!
If temperature increases, pressure MUST increase. If temperature decreases, pressure MUST decrease. Verify your answer makes physical sense!
P₁/T₁ = P₂/T₂ at constant volume. Pressure and temperature are directly proportional - when one goes up, the other goes up.
Gay-Lussac's Law requires an absolute temperature scale. 0 K is absolute zero - no molecular motion. Using °C would incorrectly suggest zero pressure at 0°C!
Higher temperature = faster molecular motion = molecules hit walls harder and more often. In a rigid container, this increased kinetic energy shows up as higher pressure.
Charles's Law: V and T (P constant) - container can expand. Gay-Lussac's: P and T (V constant) - rigid container. Different conditions!
If volume can change, use Charles's Law (constant P) or Combined Gas Law (P, V, and T all change). Gay-Lussac's only works for rigid containers.