Discussion
As per the International Standard Atmosphere model, which one of the following options about density variation with increase in altitude in the isothermal layer is correct?
Answer: D
In the isothermal layer, density decreases exponentially with altitude.
Combine hydrostatic balance with the ideal gas law at constant temperature \(T\):
\[ \begin{aligned} dp &= -\rho g\,dh, \quad p = \rho R T \\ \frac{d\rho}{\rho} &= -\frac{g}{RT}\,dh \\ \rho &= \rho_{1}e^{-g(h - h_{1})/RT} \end{aligned} \]
In the ISA this layer runs from 11 km to 20 km at 216.65 K. Density does not stay constant, since the pressure keeps falling; it cannot increase with height; and a linear decrease belongs to neither pressure nor density in this layer. Even in the gradient layer below, the decrease follows a power law, not a straight line.
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