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## Homework Statement

Think of earth's atmosphere as an ideal gas of molecular weight [tex]\mu[/tex] in a uniform gravitational field. Let g denote the acceleration due to gravity.

If z denotes the height above the sea level, show that the change of atmospheric pressure p with height is given by

dp/dz = p([tex]\left([/tex]-[tex]\mu[/tex]g/RT)

where,

dp = change in pressure

dz = change in height

[tex]\mu[/tex] = molecular weight

R = Universal gas constant

T = temperature

## Homework Equations

1) F = mg

2) P = F/A

3) PV = nRT

## The Attempt at a Solution

With the relation between force and pressure, I derived an expression of p in terms of m and g. Using the ideal gas law, i obtained another equation for p. I am lost in my attempt to derive dp/dz. Please help.

Thank in advance,

Priam

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