How to calculate pressure at altitude when there is 0 temperature lapse?

Question

To calculate pressure at a given altitude, the following formula is used:

$p = p_0 \cdot \left(1 - \frac{L \cdot h}{T_0} \right)^\frac{g \cdot M}{R \cdot L}$

(the values can be found here)

This formula is great, but only works completely with the US Standard Atmosphere. I really want to use ISA (International Standard Atmosphere) more, because it accounts for the dynamics of the atmosphere much better. The problem is that the Tropopause has a Lapse rate ($L$) of 0. I don't know how to get that to work in this formula because that would involve dividing by zero.

Any ideas?

Answer 1

I would not claim to understand what precisely is going on here, but other things remnaining constant, mathematically you have:

$$\lim_{L \rightarrow 0} \quad p_0 \cdot \left(1 - \frac{L \cdot h}{T_0} \right)^\frac{g \cdot M}{R \cdot L} = p_0 \cdot \exp \left( - \frac{ h \cdot g \cdot M}{T_0 \cdot R} \right)$$