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Temperature change with altitude

  1. Apr 11, 2012 #1
    Alright guys, just looking for a point in the right direction for a tutorial question.

    GIVEN VALUES:
    Temperature change with increasing altitude: 0.0065 K/m
    Temp at sea level: 15ºC
    Pressure at sea level: 101.5 kPa

    FIND:
    Atmospheric pressure at 7500m.


    So what I've done is found the temperature decrease between sea level and 7500m, so that temperature is 239.4K.

    And then tried (P1/T1)=(P2/T2), was a bit sceptical over this working.. it didn't.

    After that tried:

    ∫(1/P) dP = -∫(g/RT) dz


    Integrated that, giving:

    ln(P2/P1) = (-g/RT)(z2-z1)


    Placed in the values given/calculated, leading to:

    P = 101500*e^[(-9.81*7500)/(287*288.15)]

    P = 41.7 kPa

    ... which is a wee bit off the stated answer of 38.3 kPa.




    Any ideas?
     
  2. jcsd
  3. Apr 11, 2012 #2

    Filip Larsen

    User Avatar
    Gold Member

    Welcome to PF!

    In your second integral you should integrate T as a function of z (you have treated it as a constant). Usually one makes the substitution dz = (1/(dT/dz)) dT, where dT/dz is the constant lapse rate so that you get pressure as a function of temperature.

    Edit: I see now that you have posted outside the homework section of this forum. Please post future homework questions in the homework section to get better responses :smile:.
     
  4. Apr 22, 2012 #3
    Fantastic, thanks Filip.
     
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