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Lesson 25 · Hot gases
Temperature joins the trade
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Temperature joins the trade

Warm a gas that is FREE TO SWELL (a balloon, a piston) and the volume follows the absolute temperature: V1T1=V2T2\dfrac{V_1}{T_1} = \dfrac{V_2}{T_2} — V-one over T-one equals V-two over T-two. That is Charles's law. Warm a gas in a RIGID, sealed container and the volume cannot answer, so the pressure does: P1T1=P2T2\dfrac{P_1}{T_1} = \dfrac{P_2}{T_2} — Gay-Lussac's law. One question sorts every problem: can it swell? Free to swell is Charles; locked rigid is Gay-Lussac.

And here the kelvin doctrine collects. Heating a balloon from 20 ∘C20\,^\circ\mathrm{C} to 40 ∘C40\,^\circ\mathrm{C} does NOT double it — in honest units that is 293 K to 313 K, a gentle 7% stretch. Every wrong answer in this lesson that looks tempting is the Celsius number smuggled into a ratio. Convert first, scale second. No exceptions, no appeal.

V1T1V2T2

V1T1=V2T2\frac{V_1}{T_1} = \frac{V_2}{T_2}

  • V1V_1= Initial volume (volume)
  • T1T_1= Initial absolute temperature (temperature)
  • V2V_2= Final volume (volume)
  • T2T_2= Final absolute temperature (temperature)
Charles's Law solver →
P1T1P2T2

P1T1=P2T2\frac{P_1}{T_1} = \frac{P_2}{T_2}

  • P1P_1= Initial pressure (pressure)
  • T1T_1= Initial absolute temperature (temperature)
  • P2P_2= Final pressure (pressure)
  • T2T_2= Final absolute temperature (temperature)
Gay-Lussac's Law solver →