What is the correlation between pressure and elevation for an ideal gas?
p=p(z), p=pressure, p(z)=elevation

Explanation:

Expression for vertical fluid pressure is as follows.

                ........... (1)

where,     p = pressure

            = density

               g = acceleration due to gravity

               h = height

Since, g is negative then it means that an increase in height will lead to decrease in pressure.

Also, expression for density according to ideal gas law is as follows.

                  .......... (2)

where,         m = average mass or air molecule

                    P = pressure at a given point

                    k = Boltzmann constant

                    T = temperature in kelvin

Substituting values from equation (2) into equation (1) as follows.

Now, on applying integration on both the sides we get the following.

or,                                              

where,           = pressure at height h

                      = pressure at reference point    

Thus, we can conclude that the correlation between pressure and elevation for an ideal gas is  .        

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1 is the answer to this problem