Grade 11 Chemistry · 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 20C20\,^\circ\mathrm{C} to 40C40\,^\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.