I would like to know why hot air holds more water vapor. There is this question:

Why does hot air contain more water?

But I would like a more quantitative explanation. Ideally, an explanation based on, e.g., the perfect gas law, plus of course the intuitive reasoning behind the math. Should I ask a new question or should I put a bounty?

I don't have much reputation, but I could sacrifice it, if necessary. The only issue is that my requirements are quite different from those of the original question which doesn't mention any math. What should I do?

  • 2
    $\begingroup$ As a side note, it is unlikely that your intuition is similar to mine, so asking for intuition is too open ended. Read some of Feynman's books for good examples of how different his intuition is from, well, just about anyone reading them... $\endgroup$
    – Jon Custer
    Commented May 18, 2023 at 16:21
  • $\begingroup$ But, what you are looking for would appear to be en.wikipedia.org/wiki/Clausius%E2%80%93Clapeyron_relation $\endgroup$
    – Jon Custer
    Commented May 18, 2023 at 16:38
  • $\begingroup$ @JonCuster that equation seems to fit the bill, though the derivation is pretty long. Howewer, dP/dT (I presume P is the saturated vapor pressure?) seems to decrease (and quadratically, at that!) with respect to the temperature, according to that equation. I would say this motivates a question. $\endgroup$
    – DeltaIV
    Commented May 22, 2023 at 15:12
  • $\begingroup$ @DeltaIV I could try and answer your question, but some detail from you would be useful. (1) Are you looking for an answer at high school level? College level? Other? (2) Are you familiar with basic thermodynamics, saturation pressure? (3) Are you familiar with basic vapor/liquid equilibrium?, Raoult's law? (4) What exactly are you trying to do? Do you have a specific calculation in mind? The more information you provide, the easier it will be to answer your question. $\endgroup$
    – Themis
    Commented Jun 11, 2023 at 18:57


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