Combined Gas Law Calculator
Calculate pressure, volume, or temperature changes using P₁V₁/T₁ = P₂V₂/T₂
Combined Gas Law: P₁V₁/T₁ = P₂V₂/T₂
Leave the unknown value empty and select it from the dropdown below.
Understanding the Combined Gas Law
The combined gas law merges Boyle's law, Charles's law, and Gay-Lussac's law into one comprehensive equation. It describes how pressure, volume, and temperature of a fixed amount of gas relate to each other when conditions change. This law is essential for predicting gas behavior in real-world situations.
The Combined Gas Law Equation
P₁V₁/T₁ = P₂V₂/T₂
For a fixed amount of gas (constant n)
P₁, P₂ = Initial and final pressure (atm, kPa, mmHg)
Must use the same units for both
V₁, V₂ = Initial and final volume (L, mL, m³)
Must use the same units for both
T₁, T₂ = Initial and final temperature (K)
MUST be in Kelvin: K = °C + 273.15
Component Gas Laws
Boyle's Law (Constant T)
P₁V₁ = P₂V₂
Pressure and volume are inversely proportional at constant temperature
Charles's Law (Constant P)
V₁/T₁ = V₂/T₂
Volume and temperature are directly proportional at constant pressure
Gay-Lussac's Law (Constant V)
P₁/T₁ = P₂/T₂
Pressure and temperature are directly proportional at constant volume
Practical Example
Heating a Gas in a Container
A gas occupies 2.0 L at 1.0 atm and 273 K. If the temperature increases to 546 K and the volume decreases to 1.0 L, what is the new pressure?
- P₁ = 1.0 atm
- V₁ = 2.0 L
- T₁ = 273 K
- V₂ = 1.0 L
- T₂ = 546 K
- P₂ = ?
P₂ = (P₁ × V₁ × T₂) / (T₁ × V₂)
P₂ = (1.0 × 2.0 × 546) / (273 × 1.0)
P₂ = 1092 / 273
P₂ = 4.0 atm
The pressure quadrupled because the temperature doubled (increasing pressure) and the volume halved (also increasing pressure).
Key Concepts
⚗️ Fixed Amount of Gas
Number of moles (n) must remain constant
🌡️ Use Kelvin
Temperature MUST be in absolute scale (Kelvin)
📊 Proportional Relationships
P ∝ T (at constant V), V ∝ T (at constant P), P ∝ 1/V (at constant T)
🔄 Rearrangeable
Can solve for any of the six variables
Common Applications
- 🎈Weather Balloons: Calculate altitude changes as temperature and pressure vary
- 🚗Tire Pressure: Predict pressure changes with temperature (hot vs. cold weather)
- 🔥Combustion Engines: Calculate gas expansion in cylinders during heating
- 🏔️Altitude Effects: Understand how chips bags expand at high elevation
- 🧪Laboratory Work: Correct gas volumes to standard temperature and pressure (STP)
- 🏭Industrial Processes: Design gas storage and transfer systems
Important Notes
- • Temperature MUST be in Kelvin (not °C or °F)
- • Units for P, V can be anything, but must be consistent (P₁ and P₂ same units, V₁ and V₂ same units)
- • The amount of gas (moles) must remain constant
- • For real gases, deviations occur at high pressure or low temperature
- • This law combines into the ideal gas law: PV = nRT when n is not constant
⚗️Quick Reference
Units:
atm, L, K (or kPa, mL, K)
Formula:
P₁V₁/T₁ = P₂V₂/T₂
Constraint:
Fixed amount of gas (n = constant)
Temperature:
MUST use Kelvin
Level:
High School & College
🔗Related Calculators
📐Related Formulas
🎯Where It's Used
- 🎈
Weather Balloons
Altitude predictions
- 🚗
Automotive
Tire pressure changes
- 🧪
Laboratory
STP corrections
- 🏭
Industry
Gas storage systems