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Assume that the temperature remains esse...

Assume that the temperature remains essentially constant in the upper parts of the atmosphere. The atmospheric pressure varies with height as. (the mean molecular weight of air is M, where `P_(0)=` atmospheric pressure at ground reference)

A

`P_()e^((-3Mgh)/(2RT))`

B

`P_(0)e^((-Mgh)/(2RT))`

C

`P_(0)e^((-3Mgh)/(RT))`

D

`P_(0)e^((Mgh)/(RT))`

Text Solution

Verified by Experts

The correct Answer is:
D
Since pressure decreased with height
`dp=pgdh`
Consider a small volume `deltaV` of air of mass `Deltam`
`P Delta V=((Deltam)/(M))RT`
`P=(Deltam)/(Deltav)(RT)/(M)rArrP=(rhoRT)/(M)rArrrho=(PM)/(RT)`
`therefore dp=(PM)/(RT)g dh`
`int_(P_(0))^(P)(dP)/(P)=-(Mg)/(RT)int_(0)^(h)dh`
In `((P)/(P_(0)))=-(-Mgh)/(RT)`
`P=P_(0)e^((-Mgh)/(RT))`
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