Question

On a spring day, a middle-latitude city (about 40∘ north latitude) has a surface (sea-level) temperature of 10 ∘c. if vertical soundings reveal a nearly constant environmental lapse rate of 6.5 ∘c per kilometer and a temperature at the tropopause of –55 ∘c, what is the height of the tropopause?

Answer 1

Answer:

10 km

Explanation:

We are told that the temperature at the surface is

$T_0 = 10^{\circ}$

and that the rate of drop of the temperature vs height is

$k=-6.5^{\circ}/km$

Therefore we can write the temperature at a generic altitude h as

$T(h) = T_0 + kh$

If we call h the height of the tropopause, we have

$T(h) = -55^{\circ}$

Therefore we can solve the equation to find h, the height of the tropopause:

$h=\frac{T(h)-T_0}{k}=\frac{-55-10}{-6.5}=10 km$