P

where the constant P0 is usually taken as the standard sea-level pressure (105 N m-2). The significance of the potential temperature is that it is constant during processes which do not change entropy. Figure 2.105 shows an example of latitude variations of 9* and T* based on the same data.

The first law of thermodynamics states that the change in internal energy per unit mass is given by

where Q is the amount of heat added to the system (an air parcel of unit mass) per second. As in (2.47), the molecular friction (which also produces heat) will be left out. From the definition of specific entropy s, one obtains

T ds = Cp dT - p-1 dP, and by introducing the potential temperature (2.51), ds = Cp 9 - d9.

Inserting this into (2.52), the time derivative of O is obtained, dO_ Q (P0 -cv) 7cp dt Cr

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