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Lesson 37 · Relative Humidity
The air's sponge
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The air's sponge

Air holds water as invisible vapour, and how much it CAN hold depends on temperature: warm air is a bigger sponge. The ceiling is called the saturation vapour pressure, psatp_{sat} — say it p-sat — and it climbs fast with warmth: about 2.5 kPa at 21 °C, 3.0 kPa at 24 °C, 4.0 kPa at 29 °C. The vapour actually present has its own pressure, pvp_v — p-vee — and it can never beat the ceiling.

Relative humidity is simply how full the sponge is: RH=pvpsat\mathrm{RH} = \dfrac{p_v}{p_{sat}} (read aloud: R-H equals p-v over p-sat — then dress the fraction as a percentage. A ratio of pressure over pressure means every unit cancels: RH travels as a naked percent. And notice the sneaky consequence: warm the air without adding a single drop and RH FALLS, because the ceiling rose while the water stayed put. That one idea explains dry winter classrooms and the next lesson's fog.

tpvpwsφ

φ=pvpws\varphi = \frac{p_v}{p_{ws}}

  • φ\varphi= Relative humidity
  • pvp_v= Water vapour partial pressure (pressure)
  • pwsp_{ws}= Saturation vapour pressure (pressure)
Relative Humidity from Vapour Pressure solver →
pwst

pws=610.94exp⁡ ⁣(17.625 tt+243.04)p_{ws} = 610.94 \exp\!\left(\frac{17.625\,t}{t + 243.04}\right)

  • pwsp_{ws}= Saturation vapour pressure (pressure)
  • tt= Temperature (temperature)
Saturation Vapour Pressure (Magnus / Alduchov–Eskridge) solver →