What Does SI Units of Nitrogen Masses Mean in Scale Height Calculations?

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SUMMARY

The discussion centers on calculating the scale height (H) of a planet using the formula H = kT/Mg, where k is the Boltzmann constant, T is the surface temperature, g is the acceleration due to gravity, and M is the mean molecular mass. The confusion arises regarding the definition of M, specifically whether it refers to the mass of a single nitrogen molecule or the molar mass. It is clarified that M should represent the mass of one molecule, not the molar mass, as indicated by the context of the formula involving k. The participant also notes the atmospheric composition of the planet is similar to Earth's, comprising 78% nitrogen and 21% oxygen.

PREREQUISITES
  • Understanding of the Boltzmann constant (k)
  • Knowledge of scale height calculations in atmospheric physics
  • Familiarity with molecular mass and its significance in gas laws
  • Basic principles of atmospheric composition and density
NEXT STEPS
  • Research the calculation of mean molecular mass for atmospheric gases
  • Learn about the ideal gas law and its application in atmospheric science
  • Explore the relationship between scale height and atmospheric pressure
  • Investigate the use of the gas constant R in thermodynamic equations
USEFUL FOR

This discussion is beneficial for students in atmospheric science, physicists working on planetary atmospheres, and anyone interested in understanding scale height calculations and molecular mass in gas laws.

Breedlove
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Homework Statement



I want to try to find the scale height of a planet using H=kT/Mg, where H is the scale height, k is the Boltzmann constant, T is the surface temperature, g is the acceleration of gravity, and M is the mean molecular mass.

I am having a great deal of trouble understanding M and how to calculate it. In my handout, it says that it should be in units of nitrogen masses. On wikipedia it says that it should be in kg. Wikipedia also refers to mean molecular mass as being defined in terms of the unified atomic mass unit. Augh...

I know that the composition of the atmosphere is similar to ours, 78% nitrogen and 21% oxygen, but I don't know the density which prevents me from just plugging it into the ideal gas law.

Do you think that when my handout says "in SI units of nitrogen masses" it means molar masses or just the mass of one atom?

I think in the end it is safe for me to assume that the density is the same, as the planet has similar characteristics to Earth in it's radius and mass. I would really like to figure this out independent of any unnecessary assumptions though. Thanks for any help you can provide!
 
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Breedlove said:

Homework Statement



I want to try to find the scale height of a planet using H=kT/Mg, ...
.
.
.
Do you think that when my handout says "in SI units of nitrogen masses" it means molar masses or just the mass of one atom?

It would be the mass of one molecule (not necessarily a single atom, but definitely not the molar mass.)

Just FYI, when a formula has k in it, they are referring to single atoms or molecules. When they want you to use molar quantities, the gas constant R=NAk is used instead.
 

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