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Thermodynamics problem; App of 1st law, work, adiabatic processes, and enthalpy

  1. Oct 4, 2005 #1
    The question is as follows:

    the partial derivative (given as a partial, but i dont know the notation, so letter d is really little delta for the partial)

    (du/dT)p = Cp - P(Beta)v​

    where Beta = expansivity coefficient = 1/v (dv/dT)p

    again, all the "d's" are lowercase delta's for the partial derrivatives, and the "p's" next to the partials and the one with the Cp are to signify that pressure is constant.

    I know i need to start with enthalpy, dh, but im pretty much stuck. if someone would point me in the right direction i would be much obliged. thanks :devil:
     
  2. jcsd
  3. Oct 5, 2005 #2

    Astronuc

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    Staff: Mentor

    It appears that one is trying to show the relationship:

    (du/dT)p = Cp - P(Beta)v

    or

    [tex](\frac{\partial u}{\partial T})_p = c_p - p\beta v[/tex]

    where

    [tex]\beta = \frac{1}{v} (\frac{\partial v}{\partial T})_p [/tex]


    OK, how about starting with [tex] h = u + pv [/tex], or

    [tex] u = h - pv [/tex]

    differentiating with respect to T at constant P,

    [tex] (\frac{\partial u}{\partial T})_p = (\frac{\partial h}{\partial T})_p - (\frac{\partial (pv)}{\partial T})_p [/tex]

    and go from there remembering the definition of [itex]c_p[/itex] is

    [tex] c_p = (\frac{\partial h}{\partial T})_p[/tex]
     
  4. Oct 5, 2005 #3
    thanks

    duh, thank a lot. i see it clearly now. much thanks
     
  5. Oct 5, 2005 #4

    Astronuc

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    Staff: Mentor

    I have those moments too. :biggrin:
     
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