Combined Gas Law Calculator
Calculate gas state changes when pressure, volume, and temperature all vary using P₁V₁/T₁ = P₂V₂/T₂. Combines Boyle's, Charles's, and Gay-Lussac's laws for general gas calculations.
Minimum: 0
Must be greater than 0
Must be greater than 0
Results
Final Volume
6.667 L
How to Use This Calculator
Enter your input values
Fill in all required input fields for the Combined Gas Law Calculator. Follow the units and input format printed next to each field. Where a unit selector is available, choose the units that match your data.
Review your inputs
Double-check that all values are correct and match the units or format shown for each field. Incorrect units are the most common source of calculation errors and can produce results that are off by factors of 2, 10, or more.
Read the results
The Combined Gas Law Calculator computes the output in your browser and displays the results, with units clearly labeled, as soon as they are ready — no data sent to a server.
Explore parameter sensitivity
Try adjusting individual input values to see how the output changes. This is a quick and effective way to develop intuition about how different parameters influence the result and to identify which inputs have the largest effect.
When to Use This Calculator
- •Use the Combined Gas Law Calculator when you need accurate results quickly without the risk of manual computation errors or unit conversion mistakes.
- •Use it to verify calculations made by hand or in spreadsheets — an independent check can catch errors before they lead to costly decisions.
- •Use it to explore how changing input parameters affects the output — a quick way to develop intuition and identify the most influential variables.
- •Use it when collaborating with others to ensure everyone is working from the same numbers and applying the same assumptions.
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About Combined Gas Law Calculator
The Combined Gas Law Calculator handles situations where pressure, volume, and temperature all change simultaneously for a fixed amount of gas. By combining Boyle's law (P and V at constant T), Charles's law (V and T at constant P), and Gay-Lussac's law (P and T at constant V) into a single equation, it provides the most general relationship between gas state variables. This equation is essential for analyzing gas behavior in engines, weather systems, aerospace applications, and industrial chemical processes where multiple variables change simultaneously.
The Math Behind It
Formula Reference
Combined Gas Law
P₁V₁/T₁ = P₂V₂/T₂
Variables: P = pressure, V = volume, T = temperature (Kelvin); subscripts 1 and 2 denote initial and final states
Worked Examples
Example 1: Weather Balloon
P₁ = 1 atm, V₁ = 10 L, T₁ = 300 K; rises to P₂ = 0.5 atm, T₂ = 250 K
Balloon expands to 16.67 L despite cooling.
Example 2: Compressed Gas Heating
P₁ = 1 atm, V₁ = 10 L, T₁ = 300 K; compressed to P₂ = 2 atm and heated to 400 K
Volume decreases to 6.667 L.
Common Mistakes & Tips
- !Using Celsius instead of Kelvin for temperature — all gas law calculations require absolute temperature.
- !Mixing units — pressure must be in the same units on both sides, as must volume.
- !Applying the combined gas law to adiabatic processes — use PV^γ = constant instead.
- !Forgetting that the gas amount must be fixed — no leaks or chemical reactions changing moles.
Related Concepts
Used in These Calculators
Calculators that build on or apply the concepts from this page:
Frequently Asked Questions
When should I use the combined gas law vs the ideal gas law?
Use the combined gas law when comparing two states of the same gas sample (you know initial conditions and want final conditions). Use PV = nRT when you know the amount of gas (moles) and want to find P, V, or T directly.
Why does a weather balloon expand as it rises?
Atmospheric pressure decreases with altitude faster than temperature does. Even though cooling reduces volume (Charles's law), the pressure drop increases it more (Boyle's law). The net effect is expansion.
Does the combined gas law work for mixtures?
Yes, if the mixture behaves ideally. Use the total pressure and total volume. Each component obeys the law independently (Dalton's law of partial pressures).
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