Under adiabatic condition, §Q = 0, and (3.2.2) may be written dU + pdV = 0 (3.4.1)
If U is expressed as a function of p and V, we can obtain a relationship between p and V by substituting for dU from (3.3.1) and making use of the equation of state (2.4.1). Thus:
If we denote the ratio of the specific heats, cp/cv, by y, then by integrating (3.4.2) we get pVY = poVoY = Const (3.4.3)
Since y has a value of 1.4 for dry air, the adiabatic curves are steeper than the isothermals in a pV-diagram.
The adiabatic relationships between T and V, or between p and T, can be found from (3.4.3) and the equation of state for dry air. These are:
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