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Lesson 26 · The combined gas law
All three knobs at once
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All three knobs at once

Real gases rarely change one thing at a time. A balloon that climbs meets thinner air AND colder air together. The combined gas law takes it in one trip: P1V1T1=P2V2T2\dfrac{P_1 V_1}{T_1} = \dfrac{P_2 V_2}{T_2} — Boyle's ratio and Charles's ratio stacked. Cover the temperatures with a thumb and Boyle looks back at you; cover the pressures and there is Charles. It is not a third law to memorize — it is the two you know, holding hands.

Two working nuggets. First: inside a RATIO, matching units cancel — millilitres over millilitres is as honest as litres over litres, so mixed-unit problems often need no conversion at all. The one non-negotiable exception is temperature: kelvin, always, because only kelvin ratios mean anything. Second: solve algebraically FIRST, then substitute — six knobs is too many to juggle numerically, and the rearrangement is where the marks live.

P1V1T1P2T2V2

P1V1T1=P2V2T2\frac{P_1 V_1}{T_1} = \frac{P_2 V_2}{T_2}

  • P1P_1= Initial pressure (pressure)
  • V1V_1= Initial volume (volume)
  • T1T_1= Initial absolute temperature (temperature)
  • P2P_2= Final pressure (pressure)
  • V2V_2= Final volume (volume)
  • T2T_2= Final absolute temperature (temperature)
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