Calculate pressure of Atmosphere

[tracyfan_1]

Homework Statement

Calculate the pressure of the atmosphere (with approximately plane parallel slab ge-
ometry) as a function of height z above the ground. Assume the gas in the atmosphere has
constant temperature T and that the equation of state is that of an ideal gas, namely


where p and  denote the pressure an density of the gas, respectively. Here kb is Boltzmann's
constant and  is the mean molecular weight of the gas which we take to be constant
everywhere.

Homework Equations

I do not know even how to begin this question. I would really like some help on how to approach this problem.

The Attempt at a Solution

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[granpa]

the pressure at point p is equal to the weight of air above it.

the weight of a parcel of air at point p is proportional to the pressure at that point.

i.e. the function must be its own integral