Gay-Lussac's Law Calculator
Calculate pressure and temperature relationships in ideal gases at constant volume
Gay-Lussac's Law Calculation
Initial State
Final State
Optional: Calculate Number of Moles
Results
Gay-Lussac's Law Formula
Example Calculation
Heating a Metal Can
Problem: A metal can contains 300 mL of air at 20°C and 100 kPa. The can is heated to 400°C. What is the final pressure?
Given:
• Initial pressure (p₁): 100 kPa
• Initial temperature (T₁): 20°C = 293.15 K
• Final temperature (T₂): 400°C = 673.15 K
• Volume: constant (rigid container)
Solution
Using Gay-Lussac's Law: p₁/T₁ = p₂/T₂
Rearranging: p₂ = p₁ × (T₂/T₁)
p₂ = 100 kPa × (673.15 K / 293.15 K)
p₂ = 100 kPa × 2.296
p₂ = 229.6 kPa
The pressure more than doubles due to the significant temperature increase!
Key Concepts
Pressure Law
Pressure ∝ Temperature (at constant volume)
Isochoric Process
Volume remains constant
Absolute Temperature
Must use Kelvin scale
Ideal Gas
Assumes ideal gas behavior
Real-World Examples
Pressure Cookers
Higher temperature increases pressure for faster cooking
Tire Pressure
Pressure changes with temperature seasons
Aerosol Cans
Can explode if heated due to pressure increase
Hot Air Balloons
Heating air increases pressure and provides lift
Understanding Gay-Lussac's Law
What is Gay-Lussac's Law?
Gay-Lussac's Law, also known as the pressure law, describes the relationship between pressure and temperature of an ideal gas when volume and amount remain constant. It states that pressure is directly proportional to absolute temperature.
Mathematical Relationship
The law can be expressed as p/T = constant, or more commonly as p₁/T₁ = p₂/T₂ for comparing two states of the same gas sample.
Important Conditions
Constant Volume:
Container must be rigid and sealed
Constant Amount:
No gas enters or leaves the system
Absolute Temperature:
Temperature must be in Kelvin scale
Ideal Gas Behavior:
Assumes no intermolecular forces
Historical Context
Named after French physicist Joseph Louis Gay-Lussac (1778-1850), this law was discovered independently by him and Jacques Charles. It's one of the fundamental gas laws that led to the development of the ideal gas law.
Safety Note
Understanding Gay-Lussac's Law is crucial for safety when dealing with sealed containers and gases. Heating sealed containers can lead to dangerous pressure increases that may cause explosions.