Combined Gas Law
Combines Boyle, Charles and Gay-Lussac.
Formula
Variables
Example
A gas at 1 atm, 300 K, 2 L heated to 600 K at 2 atm occupies (1·2·600)/(300·2) = 2 L.
How it works
This relation links a gas’s pressure, volume, and absolute temperature when the amount of gas stays constant. It comes from combining the three simpler gas laws: pressure and volume vary inversely (Boyle), volume and temperature vary directly (Charles), and pressure and temperature vary directly at fixed volume (Gay-Lussac), so the product P·V divided by T stays constant between two states. Temperatures must be in kelvin because the law depends on absolute temperature, not Celsius.
When to use it
Use it when the same gas sample changes pressure, volume, and temperature from one state to another and no gas is added or lost. It is common in chemistry, physics, and engineering problems involving compressed gases, balloons, cylinders, weather, and laboratory setups.
Worked example, step by step
A sample of gas has an initial pressure of 0.95 atm, volume of 4.0 L, and temperature of 290 K. It is changed to a pressure of 1.40 atm and temperature of 350 K; find the new volume. Start with the combined gas law: (P1V1)/T1 = (P2V2)/T2 Substitute the values: (0.95 × 4.0)/290 = (1.40 × V2)/350 Compute the left side: 3.8/290 = 0.01310... Solve for V2: V2 = (3.8/290) × 350 / 1.40 V2 = 3.28 L Final answer: the gas occupies about 3.3 L.
Common mistakes to avoid
- Using degrees Celsius instead of kelvin for temperature
- Forgetting to keep the same amount of gas throughout the process
- Mixing up which quantities are initial and final when substituting into the equation
Did You Know?
The combined gas law is why a sealed bag of chips puffs up on an airplane as cabin pressure drops.
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More in Thermodynamics & Heat
View allHeat Energy
BasicHeat needed to change a substance’s temperature.
Latent Heat
IntermediateHeat for a phase change at constant temperature.
Ideal Gas Law
IntermediateRelates pressure, volume, moles and temperature.
Boyle's Law
BasicPressure and volume are inversely related at constant T.
Charles's Law
BasicVolume is proportional to temperature at constant P.
Gay-Lussac's Law
IntermediatePressure is proportional to temperature at constant V.