1.

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))`

Answer» Correct Answer - 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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