🔬 Combined Gas Law Calculator
Calculate the relationship between pressure, volume, and temperature of an ideal gas with constant amount. Enter any five of the six variables (P₁, V₁, T₁, P₂, V₂, T₂) and the calculator will find the sixth using the formula P₁V₁/T₁ = P₂V₂/T₂. Temperatures must be in Kelvin for accurate results.
What Is the Combined Gas Law?
The Combined Gas Law combines Boyle's Law (pressure-volume at constant temperature), Charles's Law (volume-temperature at constant pressure), and Gay-Lussac's Law (pressure-temperature at constant volume) into a single equation that relates all three variables — pressure, volume, and temperature — for a fixed amount of gas:
P₁ V₁ / T₁ = P₂ V₂ / T₂
where P is pressure, V is volume, and T is absolute temperature (Kelvin). Subscript 1 denotes initial conditions and subscript 2 denotes final conditions.
The Combined Gas Law can also be written in the form:
PV / T = k
where k is a constant for a given amount of gas.
Key characteristics of the Combined Gas Law:
- Constant amount: The number of moles of gas must remain constant.
- Absolute temperature: Temperature must be in Kelvin (K) — Celsius and Fahrenheit do not work because they are not absolute scales.
- General applicability: Any two of the three variables (P, V, T) can change simultaneously, and the law predicts the resulting changes.
How to Use This Calculator
This calculator solves for any one of the six variables in the Combined Gas Law:
- P₁, V₁, T₁ — Initial pressure, volume, and temperature
- P₂, V₂, T₂ — Final pressure, volume, and temperature
To use the calculator:
- Select which variable you want to solve for using the dropdown.
- Enter the five known values in the corresponding input fields.
- Press "Calculate" to find the missing value.
- The calculator will show the step-by-step solution and the final result.
For example, to find the final volume when a gas at 1.0 atm and 2.0 L is heated from 300 K to 600 K while pressure increases to 2.0 atm:
V₂ = P₁ V₁ T₂ / (T₁ P₂)
V₂ = 1.0 × 2.0 × 600 / (300 × 2.0)
V₂ = 1200 / 600
V₂ = 2.0 L
Real-World Applications
- Weather balloons: As a balloon rises, atmospheric pressure decreases and temperature drops, causing the balloon to expand significantly.
- Scuba diving: As a diver descends, pressure increases and temperature decreases, affecting the volume of air in the tank and lungs.
- Sealed food packaging: Bags of chips puff up at high altitudes because the pressure inside remains constant while the external pressure drops.
- Fire extinguishers: A fire extinguisher left in a hot car can reach dangerously high pressures, potentially rupturing the container.
- Refrigeration and air conditioning: The compression and expansion of refrigerant gases relies on the relationships described by the gas laws.
- Tire pressure: Tire pressure changes with temperature — approximately 1 PSI per 10°F change.
❓ Combined Gas Law FAQ
What is the Combined Gas Law formula?
The formula is P₁V₁/T₁ = P₂V₂/T₂. It combines Boyle's Law, Charles's Law, and Gay-Lussac's Law into a single equation.
Why must temperature be in Kelvin?
The Combined Gas Law uses absolute temperature. Celsius and Fahrenheit are relative scales that start at arbitrary points, so they break the proportional relationship. Always convert to Kelvin using K = °C + 273.15.
What are the conditions for the Combined Gas Law?
The law applies when the amount of gas (moles) is constant. Pressure, volume, and temperature can all change simultaneously.
How is the Combined Gas Law different from the Ideal Gas Law?
The Ideal Gas Law (PV = nRT) relates pressure, volume, temperature, and the number of moles. The Combined Gas Law is a special case of the Ideal Gas Law where the amount of gas (n) is constant.
What is the difference between gauge pressure and absolute pressure?
Gauge pressure is measured relative to atmospheric pressure. Absolute pressure includes atmospheric pressure. For gas law calculations, use absolute pressure (add atmospheric pressure to gauge readings).
Can I use this calculator for real gases?
The Combined Gas Law is accurate for ideal gases at moderate pressures. Near liquefaction or at very high pressures, real-gas corrections are needed.
What are the units for pressure and volume?
Any consistent units can be used for pressure and volume, as long as they are consistent on both sides of the equation. This calculator supports atm, kPa, bar, psi, Pa, and torr for pressure, and L, mL, m³, and ft³ for volume.
How accurate is this calculator?
This calculator uses the exact formula P₁V₁/T₁ = P₂V₂/T₂. Accuracy depends on the precision of the input values. You can adjust the decimal precision in the output.
Is this calculator free?
Yes, this calculator is completely free to use. No registration or personal data storage is required.
Who discovered the Combined Gas Law?
The Combined Gas Law is a combination of the work of Robert Boyle (1662), Jacques Charles (1787), and Joseph Louis Gay-Lussac (1809). It was later formalized as a single equation relating all three variables.