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

[Breedlove]

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 Boltzman 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!

 

[Redbelly98]

Homework Statement

I want to try to find the scale height of a planet using H=kT/Mg, ...
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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=N_Ak is used instead.

 

[tomcue]

I understand your confusion and frustration with the units and calculations involved in finding the scale height of a planet. The mean molecular mass, also known as the molar mass, is a measure of the average mass of all the atoms in a molecule. It is typically measured in units of grams per mole (g/mol). In this case, the units of nitrogen masses likely refer to the molar mass of nitrogen, which is approximately 14 g/mol. This is the value you would use in your calculation.

As for the density, it is an important factor in calculating the scale height and can vary depending on the composition of the atmosphere. In this case, it would be best to research the specific planet you are studying to determine the density of its atmosphere. This information can often be found in scientific databases or published research articles.

In order to avoid unnecessary assumptions, it is always best to use accurate and specific values in your calculations. However, if you are unable to find the exact density for your planet, using the density of Earth's atmosphere as a general approximation may still provide a reasonable estimate for your scale height calculation. Overall, it is important to carefully consider the units and values used in scientific calculations to ensure accuracy and validity of your results.