Dismiss Notice
Join Physics Forums Today!
The friendliest, high quality science and math community on the planet! Everyone who loves science is here!

Homework Help: Derive Gibbs function for dry air .

  1. Sep 22, 2011 #1
    1. The problem statement, all variables and given/known data

    1. Derive the Gibbs function g(T,P) for dry air. T = temp, P = pressure
    2. Derive the speed of sound (c) from the Gibbs function. Plot c as a function of temp and pressure.

    2. Relevant equations

    c = gp*squareroot(gTT/(g^2TP - gTT*gpp)

    I wasn't sure how to type it in but gp,gTT, etc. are partial derivatives with repect to p,TT, etc.

    g = I - T*entropy +P*specific volume



    3. The attempt at a solution

    I am having trouble getting g in terms of just P and T. I kind of did it, but I'm not sure exactly where I should end up.

    Also I am not getting anything for c that makes sense.
     
  2. jcsd
  3. Sep 22, 2011 #2

    rude man

    User Avatar
    Homework Helper
    Gold Member

    If someone gave me T and P I would go to a table of entropies and enthalpies for dry air and compute g(T,p) = h(T,p) - Ts(T,p). Nice that h and s are state functions!

    There are several formulas to derive entropies and enthalpies if you assume an ideal gas.
     
Share this great discussion with others via Reddit, Google+, Twitter, or Facebook