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

In summary, the conversation is about finding the scale height of a planet using the formula H=kT/Mg and the confusion regarding the calculation of M, which is the mean molecular mass. The person is unsure whether M should be in units of nitrogen masses or in kg. It is clarified that it should be the mass of one molecule and not the molar mass. The use of the gas constant k indicates the use of single atoms or molecules, not molar quantities. The person also mentions assuming the density to be similar to Earth's in order to solve the problem.
  • #1
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 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!
 
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  • #2
Breedlove said:

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=NAk is used instead.
 
  • #3


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.
 

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

What is scale height for planets?

Scale height is a measure of how quickly the density of a planet's atmosphere decreases with increasing altitude. It is typically defined as the height at which the atmospheric pressure has decreased by a factor of e, or about 2.718.

How is scale height calculated?

Scale height can be calculated using the ideal gas law, which relates pressure, temperature, and density. It is also dependent on the mass of the planet and the composition of its atmosphere. There are also more complex models that take into account factors such as gravity and atmospheric escape.

Why is scale height important?

Scale height is important because it helps us understand the structure and behavior of a planet's atmosphere. It can also provide insight into the planet's history and evolution. Scale height can also be used to estimate the atmospheric thickness and the potential for habitability on a planet.

How does scale height differ between planets?

The scale height for a planet's atmosphere can vary greatly depending on its size, mass, and composition. For example, smaller planets with weaker gravity tend to have higher scale heights, while larger planets with stronger gravity have lower scale heights. The composition of the atmosphere also plays a role, as heavier gases tend to have lower scale heights than lighter gases.

Can scale height change over time?

Yes, scale height can change over time due to a variety of factors such as changes in a planet's atmosphere, temperature, and gravity. For example, if a planet's atmosphere is being eroded by solar wind, its scale height may decrease over time. Additionally, changes in a planet's climate can also affect its scale height.

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