### Thermodynamics Is Fun

1. Define potential temperature for a fluid.
2. Express the potential temperature of an ideal gas as a function of its temperature and pressure.
3. Derive the adiabatic lapse rate $$\Gamma_{\text{ad}}$$ for an ideal gas (in hydrostatic balance).
4. Discuss the behaviour of the fluid when the actual lapse rate $$\Gamma > \Gamma_{\text{ad}}$$ and $$\Gamma < \Gamma_{\text{ad}}$$.

From Wikipedia.

From Wikipedia.