Show that the ideal gas law can be rewritten as P = where p is the density and M

Question

Show that the ideal gas law can be rewritten as P = where p is the density and M is the molar mass in kg. {M for N2 = 0.028 kg/mol} Consider a layer of atmosphere some height h above the surface of a planet and having thickness Deltah. Find an expression for DeltaP = P(h+ Deltah h) - P(h), the pressure difference between the top and the bottom surfaces of the layer being considered using ideas about fluids and density. Use the modified ideal gas law to substitute for the density and integrate the resulting equation to obtain a function for P(h). Again use the modified ideal gas law to get an expression for the density p(h).

Explanation / Answer

    P=(nRT)/V

     p=M/V

    V=M/p

     P=(pRT)/M

   

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