A.  Latent Heats.

For water to change phase from solid to liquid to vapor, external energy must be supplied to break chemical bonds, called hydrogen bonds, that hold the water molecules together.  Conversely, as water vapor becomes liquid and as liquid water becomes ice, energy is given off by water as the chemical bonds form.  This energy is often called the latent heat, but is also known more properly as the enthalpy.

The energy required to convert ice to liquid water is called the latent heat of melting, which has a value of 3.34x10⁵ J/kg.  This is also called the latent heat of fusion.

The energy required to convert liquid ice to vapor is called the latent heat of vaporization, which has a value of 2.50x10⁶ J/kg.  This is also called the latent heat of condensation.

Compare these values to the specific heats of dry air (c_p = 1004 J/K/kg), of liquid water (c = 4218 J/K/kg), and of ice (c = 2106 J/K/kg).  These are about 100 to 1000 times smaller.  No wonder that we get much more energy, or take up so much more energy with a phase change compared to the heating or cooling of a substance.
 

B. Adiabatic Processes

An adiabatic process is one in which no energy is added and taken out of an air parcel by the surrounding air or ground.  An air parcel is a figment of our imagination -- no such thing exists, at least not for long.  But we can use the idea of a small air parcel in order to gain some understanding about what happens when air moves vertically through the atmosphere.

For this discussion on adiabatic processes, we assume that the air parcel has the following properties:
1. No energy is exchanged with its environment;
2. It has the same pressure as the environment at the sane level (it is in hydrostatic equilibrium.).
3. It moves slowly enough that its kinetic energy is only a small part of its total energy.
 

C. Adiabatic Lapse Rate

Remember that by the First Law of Thermodynamics, dq = c_p dT - adp = 0.

Rearranging this expression, and using the expression for hydrostatic equilibrium, we find:

This has a value of 9.8 K/km.  Air parcels that are rising or sinking adiabatically will change temperature with altitude as this rate.
 

D. Potential Temperature

Potential temperature is a very useful concept, even more useful than virtual temperature.  The potential temperature is the temperature that an air parcel would have if it were expanded or compressed adiabatically from its existing pressure and temperature to a standard pressure, taken as 1000 hPa.  I will not go through the derivation, by the potential temperature is given by the expression:

Why is potential temperature so useful?  If an air parcel exchanges no energy with its environment, then it will retain the same potential temperature as its rises (and expands and cools) and falls (and compresses and warms).  Potential temperature is a conserved quantity of the air parcel.  In many atmospheric processes, potential temperature is approximately conserved.