How to Use Combined Gas Law Calculator
The Combined Gas Law Calculator finds the unknown variable when you know the other five values describing two states of the same gas sample. It applies Boyle’s, Charles’s, and Gay-Lussac’s laws simultaneously.
- Choose the unknown - Tell the Combined Gas Law Calculator which of P₁, P₂, V₁, V₂, T₁, T₂ you want to solve for. The calculator grays out the selected field and solves for it.
- Enter the five known values - Use consistent units; the Combined Gas Law Calculator handles atm/Pa/kPa for pressure, L/mL/m³/cm³ for volume, and K/°C/°F for temperature — converting everything internally to SI.
- Verify with the formula card - The results panel displays the rearranged equation the calculator used, so you can confirm the algebra by hand or use it as a homework template.
- Compare scenarios by iterating - The Combined Gas Law Calculator runs entirely in your browser, so change one variable at a time to quickly explore how pressure, volume, and temperature trade off against each other.
Formula & Theory - Combined Gas Law Calculator
The Combined Gas Law Calculator is built on the single algebraic identity:
P₁ · V₁ / T₁ = P₂ · V₂ / T₂| Symbol | Meaning |
|---|---|
| P₁, P₂ | Absolute pressures in states 1 and 2 |
| V₁, V₂ | Volumes in states 1 and 2 |
| T₁, T₂ | Absolute temperatures (kelvin) |
This identity combines three classic laws: Boyle’s (PV constant at constant T), Charles’s (V/T constant at constant P), and Gay-Lussac’s (P/T constant at constant V). It assumes the amount of gas n stays the same in both states.
Degenerate Cases
When one variable is held constant, the combined law reduces to a familiar special case:
| Held constant | Law | Relationship |
|---|---|---|
| T (isothermal) | Boyle’s Law | P₁V₁ = P₂V₂ |
| P (isobaric) | Charles’s Law | V₁/T₁ = V₂/T₂ |
| V (isochoric) | Gay-Lussac’s Law | P₁/T₁ = P₂/T₂ |
The Combined Gas Law Calculator covers all three as special cases — simply enter equal values for the constant quantity.
Worked Example
A gas at P₁ = 1 atm, V₁ = 2 L, T₁ = 300 K is compressed to P₂ = 3 atm and cooled to T₂ = 200 K. Find V₂:
V₂ = P₁ · V₁ · T₂ / (T₁ · P₂)
= 1 × 2 × 200 / (300 × 3)
= 400 / 900 ≈ 0.444 LAssumptions and Limits
The calculator assumes an ideal gas, fixed amount, and absolute temperature. Real gases deviate near the critical point, at very high pressure, or when intermolecular forces matter; use the Van der Waals or virial equations there. Pressure must always be absolute (not gauge).
Use Cases for Combined Gas Law Calculator
The Combined Gas Law Calculator is useful when you need a quick, transparent calculation for gas-state comparisons. Common uses include:
- Scuba diving - Predict cylinder pressure after the temperature drops at depth or after a cold dive to ensure the cylinder has enough air for ascent.
- Weather balloons - Estimate the volume when a balloon ascends to thinner, cooler air, and check whether it will burst before reaching the target altitude.
- Engine cycles - Compare cylinder states during intake, compression, or exhaust strokes to estimate compression ratios and peak pressures.
- Chemistry homework - Combine Boyle’s, Charles’s, and Gay-Lussac’s relationships in one step without juggling three separate formulas.
- Tire pressure - Estimate how much tire pressure rises after a long highway drive raises the air temperature from 20 °C to 60 °C.
- Laboratory gas handling - Convert a measured gas volume at lab temperature and pressure to standard conditions (STP or NTP) for reporting.
For non-ideal behavior, switch to a real-gas calculator. For mass-flow or n-changing problems, use the full ideal gas law PV = nRT. The Combined Gas Law Calculator is your fastest route to first-pass gas-state answers across science, engineering, and everyday life.