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$$c_{p}dT + M g dz = 0,$$

$$\DD{T}{z} = - \frac{ M g }{c_{p}},$$ (21)

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$$\DD{T}{z} = - \frac{ M_{v} g }{ {c_{p}}_{d}} \left\{ \frac{ 1 + \... ...}{M_{d}} } { 1 + \frac{( {c_{p}}_{v} - {c_{p}}_{d} ) X}{{c_{p}}_{d}}} \right\}.$$ (22)

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$$\DD{T}{p} = \frac{ R T }{ c_{p} p },$$ (23)

$$\DD{T}{p} = \frac{ R T }{ {c_{p}}_{d} p } \left\{ \Dinv{ 1 + \frac{( {c_{p}}_{v} - {c_{p}}_{d} ) X}{{c_{p}}_{d}}} \right\}.$$ (24)

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$$M \approx M_{d}, \;\;\; c_{p} \approx {c_{p}}_{d}, \;\;\;$$ (25)

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$$\DD{T}{z} \approx - \frac{M_{d} g}{{c_{p}}_{d}}$$ (26)

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$$M \approx M_{v}, \;\;\; c_{p} \approx {c_{p}}_{v},$$ (27)

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$$\DD{T}{z} \approx - \frac{M_{v} g}{{c_{p}}_{v}}$$ (28)

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