Calculating mass of the atmosphere

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SUMMARY

The discussion focuses on calculating the total mass of the atmosphere between the latitudes of 25S and 25N and pressure levels of 300mb and 200mb. The method involves using the Earth's radius of 6378 km and the formula for the volume of a cylinder, πr²h. A participant attempted to estimate the heights of the pressure levels but was advised by their professor that a more precise method exists. The conversation highlights the need for a definitive approach to atmospheric mass calculations without relying on approximations.

PREREQUISITES
  • Understanding of atmospheric pressure levels, specifically 200mb and 300mb.
  • Familiarity with basic geometry, particularly the volume of a cylinder.
  • Knowledge of Earth's dimensions, including radius and latitude conversions.
  • Basic grasp of atmospheric science concepts related to mass and volume.
NEXT STEPS
  • Research the concept of hydrostatic balance in atmospheric science.
  • Learn about the Ideal Gas Law and its application in atmospheric calculations.
  • Explore advanced methods for calculating atmospheric mass without approximations.
  • Investigate the use of atmospheric models for precise pressure level analysis.
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Students in meteorology, atmospheric scientists, and educators involved in teaching atmospheric physics and calculations related to atmospheric mass.

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Homework Statement



Calculate the total atmospheric mass between 25S and 25N, between the pressure levels 300mb and 200mb. Assume the Earth is a perfect sphere.

Homework Equations



Radius of the Earth = 6378km
1 degree latitude = 111km
volume of cylinder = pi*r^2*h

The Attempt at a Solution



I have tried this solution using approximate, average heights of the 200 and 300mb pressure levels, and assuming the "band" of 25N and 25S is a cylinder. From here, I found the volume of the Earth up to 200mb and subtracted it from the volume of the Earth at 200mb, to get the volume between 200 and 300mb. However, my professor said there was a way to do this without estimating pressure heights, and I am unsure how to do this.
 
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