Derive Gibbs function for dry air .

[mj478]

Homework Statement

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.

Homework 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

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.

 

[rude man]

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.