Question

Q. If atmospheric pressure of surface of earth is $P_0$. Find pressure at height H. Molar mass of air is 'M'.

Answer 1

Dear Student,


$$\begin{gathered} thisisknwnasbarometricformula \\ Thebarometricformulacanbederivedfairlyeasilyu\sin gtheidealgaslaw: \\ pressure \\ P=\frac{\rho RT}{M} \\ assumeallpressureishydrostatic \\ dP=-\rho gdh \\ dividetheeqn \\ \frac{dP}{P}=\frac{-\rho g.dh.M}{\rho RT} \\ {\int }_{P_0}^P\frac{dP}{P}={\int }_0^h\frac{-g.dh.M}{RT} \\ \ln \left(\frac{P}{P_0}\right)=\frac{-Mgh}{RT} \\ P=P_0{e}^{\left(\frac{-Mgh}{RT}\right)} \\ henceprovedeqnisderived. \\ Regards \end{gathered}$$