사용 방법 the Combined Gas Law (P₁V₁/T₁ = P₂V₂/T₂): 공식 & 예제
Use P₁V₁/T₁ = P₂V₂/T₂ to find final 압력, volume, or temperature. 변환 °C to kelvin, keep 단위 consistent, and verify every answer with a free combined gas law calculator.
What the Combined Gas Law Means
The combined gas law connects two states of the same gas sample when the amount of gas stays fixed. In symbols: P₁V₁/T₁ = P₂V₂/T₂. 압력, volume, and absolute temperature on one side balance the same trio on the other.
It merges Boyle’s law (P and V at fixed T), Charles’s law (V and T at fixed P), and Gay-Lussac’s law (P and T at fixed V) into one home일-friendly ratio. Most 일sheet 실수s come from Celsius temperatures or mismatched 단위 — not from the algebra.
If you already have five known values and only need a 확인ed unknown, open the free combined gas law calculator first, then return here for Kelvin traps and 일ed examples.
The 공식 P₁V₁/T₁ = P₂V₂/T₂
Rearrangements that cover almost every problem:
When one quantity is unchanged, cancel it mentally: fixed volume → P/T constant; fixed 압력 → V/T constant; fixed temperature → PV constant.
Kelvin First — Always
Absolute temperature is required:
Trap: 27 °C looks “small,” but the gas law sees 300 K. Using 27 in the denominator shrinks T and warps every other unknown.
단위 That Stay Consistent
The calculator defaults (kPa, L, K) match many school labs. If your paper uses atm, convert both P₁ and P₂ the same way.
풀이 예제
예제 1: find final 압력
A gas at 100 kPa, 2.0 L, and 300 K is heated to 360 K at the same volume. P₂ = (100 × 2.0 × 360) / (300 × 2.0) = 120 kPa. Rough 확인: temperature rose 20%, so 압력 rose 20%.
예제 2: °C conversion before solving
Initial: 1.0 atm, 5.0 L, 27 °C. Final: 2.0 atm, 2.5 L, find T₂. First T₁ = 27 + 273 = 300 K. T₂ = (2.0 × 2.5 × 300) / (1.0 × 5.0) = 300 K (still 27 °C). Skipping the conversion and using 27 would be wrong.
예제 3: find final volume (Boyle 확인)
P₁ = 200 kPa, V₁ = 3.0 L, T₁ = 250 K → P₂ = 100 kPa at the same T. V₂ = (200 × 3.0 × 250) / (250 × 100) = 6.0 L. Halving 압력 at fixed T doubles volume.
Combined Gas Law vs 이상기체 Law
Use the combined law when you 비교 two states of the same sample and n is constant. Use PV = nRT when moles matter, or when you need one absolute state from P, V, n, and T instead of a before/after pair.
For mole-based problems, open the ideal gas law calculator.
흔한 실수
Sanity 확인: absolute temperatures near room conditions are roughly 270–310 K, not 20–40.
확인 With the 무료 계산기
The combined gas law calculator rearranges P₁V₁/T₁ = P₂V₂/T₂ with visible steps so you can verify home일 unknowns.
Combined gas law calculator — P₂, V₂, or T₂.
Ideal gas law calculator — PV = nRT.
압력 calculator — 힘 over area context.
학습 P₁V₁/T₁ = P₂V₂/T₂ with kelvin temperatures, then confirm every answer on the calculator.