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nincompoop

  • one year ago

why is warm air less denser than cool air? mathematical derivation

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  1. anonymous
    • one year ago
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    because the molecules in warm air move faster than cool air, creating more space for every molecule... i think... is that what you need?

  2. nincompoop
    • one year ago
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    thanks google

  3. anonymous
    • one year ago
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    lol

  4. nincompoop
    • one year ago
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    moving faster does not mean more space

  5. IrishBoy123
    • one year ago
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    you could play around with pV = nRT

  6. anonymous
    • one year ago
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    ok....

  7. nincompoop
    • one year ago
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    correct you can use pV=nRT and also use kinetic energy from those moving particles

  8. IrishBoy123
    • one year ago
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    so \(V \propto T\)

  9. IrishBoy123
    • one year ago
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    so if the air is in a confied space it retains its density but pressure increases in atmosphere air can move - pressure makes it move, so volume etc etc

  10. IrishBoy123
    • one year ago
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    and then gravity makes it move!!! wind!

  11. nincompoop
    • one year ago
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    fun stuff because we have high and low pressures in the atmosphere as well

  12. anonymous
    • one year ago
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    well you can sub n=m/M

  13. anonymous
    • one year ago
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    \[PV=\frac{ mRT }{ M }\] \[P=\frac{ mRT }{ VM }\] \[P=\frac{ \rho*RT }{ M }\]

  14. anonymous
    • one year ago
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    umm

  15. anonymous
    • one year ago
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    Assuming it is a ideal gas you can use the ideal gas equation and the definition of molar mass in the following way. First consider the ideal gas equation \[pV=RnT\] And substitute in molar amount from the definition of molar mass \[n=\frac{ m }{ M }\] This gives you \[pV=\frac{ RmT }{ M }\] Now you can isolate \[m/V\] which is the density \[\rho =\frac{ m }{ V }=\frac{ pM }{ TR }\] As you can see the density is inversely proportional to the temperature. Hopes this answers your question :)

  16. anonymous
    • one year ago
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    trying to expand on this..hmm

  17. anonymous
    • one year ago
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    well we can group M/R since they are simply constants, call it A

  18. anonymous
    • one year ago
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    \[\rho=\frac{ P }{ AT }\]

  19. anonymous
    • one year ago
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    so density is inversely proportional to temperature i reckon

  20. anonymous
    • one year ago
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    so at high Temp, density is low relative to low temp (analogous of cold and hot air)

  21. anonymous
    • one year ago
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    plus, when people usually say that hot air rises, it is actually false. it depends on the system parameters. Using the nomenclature that hot air pushes up on the cold air would be better

  22. anonymous
    • one year ago
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    and since it pushed up on the cold air, it causes the cold air to be pushed downwards

  23. anonymous
    • one year ago
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    hope this helps

  24. nincompoop
    • one year ago
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    the differential density investigate both in air and in ocean to see how temperature and density interplay.

  25. anonymous
    • one year ago
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    can we assume all pressure is hydrostatic?

  26. nincompoop
    • one year ago
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    will that explain welling effect?

  27. IrishBoy123
    • one year ago
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    i've just googled welling. never heard of it before. now that is interesting...

  28. IrishBoy123
    • one year ago
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    is that part of life on earth? stuff dredged up by wind and the coriolis force, add a dash of sunshine, keep repeating, and 3 billions years later,... the iPad!!

  29. anonymous
    • one year ago
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    hmm, my thermodynamic knowledge may have to come into this...hmm

  30. baewolfstar
    • one year ago
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    Welp I feel stupid

  31. nincompoop
    • one year ago
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    https://wiki.met.no/_media/windfarms/brostrom_jms_2008.pdf

  32. anonymous
    • one year ago
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    that feeling when you get these papers for free at uni. such a gd feeling

  33. anonymous
    • one year ago
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    nup, im done thinking

  34. anonymous
    • one year ago
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    my brain will collapse

  35. anonymous
    • one year ago
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    lel

  36. anonymous
    • one year ago
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    its an interesting one. we just take this for granted way too easily!

  37. anonymous
    • one year ago
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    i'm not sure if this help but doesn't hurt looking https://en.wikipedia.org/wiki/Barometric_formula#Density_equations

  38. anonymous
    • one year ago
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    i can only think that differential density only comes about with changes in altitude...thats why i was thinking hydrostatic pressure

  39. nincompoop
    • one year ago
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    correct

  40. nincompoop
    • one year ago
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    the rule of thumb on less dense being on top much like oil and water also apply with cool air and warm air when talking about air or air pockets and the atmosphere

  41. baewolfstar
    • one year ago
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    Yup still feel stupid

  42. anonymous
    • one year ago
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    yes

  43. nincompoop
    • one year ago
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    thank you, guys I wish I can medal you all

  44. anonymous
    • one year ago
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    i'd be interested if you could extend my knowledge on this and how we can model it! would be interesting.

  45. anonymous
    • one year ago
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    haha i can't believe you can distribute owl bucks. thats hectic

  46. anonymous
    • one year ago
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    good luck!

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