Potential Temperature
Derived directly from integration of the 1st law
of thermodynamics. It is the temperature
a parcel of air at P and T would have if it were at Ps. It is
conserved for adiabatic motions, ( i.e., d/dt = 0).
![Theta](https://pds-atmospheres.nmsu.edu/images/Theta.gif)
![kappa](https://pds-atmospheres.nmsu.edu/images/kappa.gif)
![rho](https://pds-atmospheres.nmsu.edu/images/rho2.gif)
![kappa](https://pds-atmospheres.nmsu.edu/images/kappa.gif)
![kappa](https://pds-atmospheres.nmsu.edu/images/kappa.gif)
For earth = 0.286 (<mw> = 28.96, Cp =
1.004 Joules/gram/K). Some authors write this equation with
= Cp/Cv = 1/(1-
)
![partial](https://pds-atmospheres.nmsu.edu/images/partial.gif)
![partial](https://pds-atmospheres.nmsu.edu/images/partial.gif)
![rho](https://pds-atmospheres.nmsu.edu/images/rho2.gif)
![partial](https://pds-atmospheres.nmsu.edu/images/partial.gif)
![partial](https://pds-atmospheres.nmsu.edu/images/partial.gif)
therefore,
![integ](https://pds-atmospheres.nmsu.edu/images/integ.gif)
![Theta](https://pds-atmospheres.nmsu.edu/images/Theta.gif)
![integ](https://pds-atmospheres.nmsu.edu/images/integ.gif)
if H(z) = H0
![Theta](https://pds-atmospheres.nmsu.edu/images/Theta.gif)
![kappa](https://pds-atmospheres.nmsu.edu/images/kappa.gif)