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Atmospheric Pressure

Q. If atmosph...

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Q. If atmospheric pressure of surface of earth is $P_{0}$ . Find pressure at height H. Molar mass of air is 'M'.

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Solution

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$t h i s i s k n w n a s b a r o m e t r i c f o r m u l a T h e b a r o m e t r i c f o r m u l a c a n b e d e r i v e d f a i r l y e a s i l y u \sin g t h e i d e a l g a s l a w : p r e s s u r e P = \frac{ρ R T}{M} a s s u m e a l l p r e s s u r e i s h y d r o s t a t i c d P = - ρ g d h d i v i d e t h e e q n \frac{d P}{P} = \frac{- ρ g . d h . M}{ρ R T} \int_{P_{0}}^{P} \frac{d P}{P} = \int_{0}^{h} \frac{- g . d h . M}{R T} \ln (\frac{P}{P_{0}}) = \frac{- M g h}{R T} P = P_{0} e^{(\frac{- M g h}{R T})} h e n c e p r o v e d e q n i s d e r i v e d . R e g a r d s$

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