Recall (see any standard physical chemistry text) that for adiabatic expansions or compressions of an ideal gas, there are several relationships between P, V, and T that hold; e.g., PVy = constant, where y is the ratio of the heat capacities at constant pressure and volume, i.e., y = cp/cv. Most useful in the context of potential temperature is TPy/y~ 1 = constant. Applying this latter relationship, pp(y/y- l) _ gpVy/y-'). (p)

where c /R = 3.5 for dry air. Rearranging Eq. (Q) gives t = e(.p/p0)R/c> = e(p/p{)tm\ (R)

A plot of plim' versus temperature for a given 6 is a straight line of constant potential temperature. Such plots are known as pseudoadiabatic charts when plotted with an inverted pressure scale so that pressure increases from top to bottom.

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