Combined Gas Law Calculator

Frequently Asked Questions

What is the combined gas law?

P₁V₁/T₁ = P₂V₂/T₂ for a fixed amount of gas between two states. It merges Boyle's, Charles's, and Gay-Lussac's laws.

How is it different from the ideal gas law?

PV = nRT relates one state with the amount of gas n. The combined law compares two states of the same gas sample and needs no n or R.

Why must temperature be in Kelvin?

The relationships are proportional to absolute temperature. Using °C or °F (which have arbitrary zeros) gives wrong ratios; the tool converts to K.

When does it break down?

At very high pressure or near condensation, real gases deviate from ideal behaviour and need the van der Waals or other real-gas equations.

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How This Calculator Works

The Combined Gas Law links the pressure, volume, and absolute temperature of a fixed amount of gas between two states: (P₁ × V₁) ÷ T₁ = (P₂ × V₂) ÷ T₂. It assumes the number of moles is constant - no gas is added or removed and the container does not leak. This tool solves for any one of the six quantities given the other five. Algebraically, the chosen unknown is isolated by cross-multiplying; for example, the final pressure is P₂ = (P₁ × V₁ × T₂) ÷ (T₁ × V₂). Temperatures may be entered in Kelvin, Celsius, or Fahrenheit and are converted internally - but the law only works with absolute temperature, so every T is converted to Kelvin before any arithmetic. This is the two-state "before and after" law; it is distinct from the Ideal Gas Law PV = nRT, which describes a single state and requires knowing the amount of gas n and the gas constant R.

Worked Example: Heating a Sealed Syringe

A sealed syringe holds 0.0224 m³ of gas at 101,325 Pa and 273.15 K (0°C). It is heated to 373.15 K (100°C) while the plunger is locked, so the volume stays 0.0224 m³. Solve for P₂: since V₁ = V₂, they cancel, leaving P₂ = P₁ × (T₂ ÷ T₁) = 101,325 × (373.15 ÷ 273.15) ≈ 138,425 Pa, about 1.37 atm. The pressure rose 37% purely from the temperature increase - the physical reason a sealed aerosol can warns "do not incinerate" and why car tyre pressure climbs after a long highway drive.

The Three Laws It Combines

Boyle's Law (constant T): P₁V₁ = P₂V₂ - squeeze the volume and pressure rises proportionally.

Charles's Law (constant P): V₁ ÷ T₁ = V₂ ÷ T₂ - heat a balloon and it expands.

Gay-Lussac's Law (constant V): P₁ ÷ T₁ = P₂ ÷ T₂ - heat a rigid tank and pressure climbs.

Hold any one variable fixed and the combined law collapses back into one of these three special cases.

Why Temperature Must Be Absolute

Using Celsius or Fahrenheit directly produces nonsense because those scales have arbitrary zero points. At 0°C a gas has not lost all its thermal energy - dividing by "0" would imply infinite pressure, and a negative Celsius value would give a negative ratio. The Kelvin scale starts at absolute zero (−273.15°C), where molecular motion theoretically stops, so ratios like T₂ ÷ T₁ are physically meaningful. Always convert: K = °C + 273.15. This calculator does the conversion automatically, but if you compute by hand, forgetting it is the single most common mistake.

Assumptions & Limits

The Combined Gas Law treats the gas as ideal: point-like molecules, no intermolecular forces, perfectly elastic collisions, and a sealed, fixed amount of gas. It is accurate for everyday conditions but drifts at high pressure (molecules crowd together) and low temperature (attractions matter), where the van der Waals equation does better. It cannot handle a changing number of moles - a reaction that produces or consumes gas, or a leak, breaks the assumption. It also says nothing about how fast a change happens or about phase transitions; once a gas condenses to a liquid, the law no longer applies.

Combined Gas Law Calculator

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