Deriving CpT+gz=Constant using Adiabatic Process and Thermodynamic Equations

[demonxdrums]

Using Theta=T(Pi/Pf)^K, Prove that CpT+gz=Constant using various equations of Thermodynamics.

Theta=Potential Temperature
T=Temperature
Pi=Initial Pressure
Pf=Final Pressure
K=a constant(.286)This is for an Adiabatic process(heat is not gained/lost)



The "various equations" are based on the well known primary equations of thermodynamics such as the equation of state, the 1st law of thermodynamics, etc. I'm clueless. I was out of class when this was taught. Could someone show me where to start?

 

[hunt_mat]

Is this possibly a question concerning ideal gases?