Calculate pressure of Atmosphere

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SUMMARY

The discussion focuses on calculating atmospheric pressure as a function of height (z) using plane parallel slab geometry and the ideal gas law. The key variables include pressure (p), density (ρ), temperature (T), Boltzmann's constant (kb), and mean molecular weight (μ). The solution approach emphasizes that the pressure at a given point is determined by the weight of the air above it, indicating that the pressure function must be its own integral. This establishes a direct relationship between pressure and height in the atmosphere.

PREREQUISITES
  • Understanding of the ideal gas law and its components
  • Familiarity with basic calculus, particularly integration
  • Knowledge of atmospheric physics concepts
  • Concept of hydrostatic equilibrium in fluids
NEXT STEPS
  • Study the derivation of the barometric formula for atmospheric pressure
  • Learn about hydrostatic equilibrium in the context of fluid mechanics
  • Explore the implications of temperature variations on atmospheric pressure
  • Investigate the role of Boltzmann's constant in statistical mechanics
USEFUL FOR

Students in physics or engineering disciplines, atmospheric scientists, and anyone interested in understanding the principles of atmospheric pressure calculations.

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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

m68jJ.png


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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Physics news on Phys.org
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
 

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