Temperature Variation in a Neutral Atmosphere

Let us assume that the atmosphere is in a state in which adiabatic air parcels that move vertically are always in equilibrium with their surroundings. This atmospheric equilibrium state is defined as neutral, and the corresponding temperature profile will be used as the 

We would like to calculate the temperature profile T(z) that corresponds to a neutral atmosphere. If an air parcel of mass m moves infinitesimally in the atmosphere, its change of internal energy dU satisfies the first law of thermodynamics 

To replace the term dV n (16.2) with terms that depend on temperature and pressure, we can use the ideal-gas law as pV = mRT/Mair for the air parcel. Taking the derivatives of both sides and recognizing that the mass of the air parcel by definition remains constant, 

Majr p A7a Rearranging and dividing both sides by dz, we have 

We have already derived the change of pressure with height in the atmosphere using the hydrostatic equation to derive (1.3). Substituting the dp/dz term and simplifying, we get 

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