In class we derived the rate at which temperature decreases with altitude in the

Question

In class we derived the rate at which temperature decreases with altitude in the troposphere (the
layer of the atmosphere nearest the Earth’s surface).
(a) Starting with the result from class,( result: dT/dy= - (9.7) k/km "dry adiabatic lapse rate") find an equation which expresses temperature as a function of height within the troposphere, assuming that T0 is the temperature at the earth’s surface.
(b) Starting with your result from (a), find an expression for pressure as a function of height in the troposphere, assuming that the pressure at the earth’s surface is Patm.
(c) What is the pressure difference between the surface and a point 5 km above the surface? Assume that the surface temperature is 300K.

Explanation / Answer

(1)dT/dy=-9.7
dT=-9.7dy
T-T0=-9.7y

T=T0-9.7y

(2)PV=nRT

P=nRT/V

dP=(nR/V)dT

P-Patm=(nR/V)(T-T0)

P=(nR/V)(T-T0)+Patm

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