Chapters 1 to 6 laid down the fundamental physical and mathematical concepts pertaining to thermodynamics. While we always kept the discussion close to our atmosphere, it was not until Chapter 7 that, in a more applied mood, we presented how these concepts are applied to yield quantities useful to atmospheric processes. However, even if we understand all the mathematics, we still need an efficient way to present and visualize thermodynamic processes in the atmosphere. Thermodynamic diagrams can do that. Up to this point we made an effort to visualize the thermodynamic process using a (p, V) or a (p, T) diagram. However, such diagrams, while simple, may not be very convenient when it comes to their utilization.

Since the purpose of a diagram is efficiently and clearly to display processes and estimate thermodynamic quantities, the following are very desirable in a thermodynamic diagram: (1) for every cyclic process the area should be proportional to work done or energy (area-equivalent transformations), (2) lines should be straight (easy to use), and (3) the angle between adiabats and isotherms should be as large as possible (easy to distinguish). The (p, V) diagram satisfies the first condition (pda = dw), but the angle between isotherms and adiabats is not very large (Figure 4.5(a)). Because of this, while it is used for illustration purposes, this diagram is not used in practice.

Conditions for area-equivalent transformations

When we are constructing a new diagram, in effect, we go from the x = a, y = -p domain to a new domain characterized by two new coordinates, say u and w.