Calculating Atmospheric Pressure at High Altitudes Using Quantum Mechanics

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In summary, the question asks to find the pressure in Earth's atmosphere at 20,000m, assuming a temperature of 350K. The attempted solution involves using the ideal gas law and calculating number density at sea level, but there is uncertainty about how to incorporate the mass and whether internet data should be used. Assistance is requested.
  • #1
max1995
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Homework Statement


I was given this as a homework question for my quantum mechanics section
Find the pressure in the earth’s atmosphere at 20,000m assuming the temperature is 350K.

Homework Equations

The Attempt at a Solution


First I assumed it was isothermal (we covered it in lecture so can assume that I think)
said the standard pressure at sea level is 101325Pa

number density= N/V=pressure/(kT)

so 101325/(1.38x10^-23x350) = 2.1x^25 = n0

then I was going to use n=n0e-(mgh)/(kT) but don't know how to calculate or estimate m

I did post this question before but have decided I have no real idea what to do so I am reposting it now (not sure if this is allowed so sorry if it isn't)

1. Homework Statement

Find the pressure in the earth’s atmosphere at 20,000m assuming the temperature is 350K

Homework Equations

The Attempt at a Solution


I use PV=NkT

P/kT=N/V but as N/V = number density at sea level (n0)

the number density (n0) = 101365/(1.38x10-23*350 = 2.1x10^25

and then I would of used n=n0*e-mgh/kT but 1. don't think this is the right way to do it (if it is could someone please say) and also don't know the mass without having to use loads of numbers pulled from the internet, which isn't normally done in my physics worksheets

Thanks for any help
 
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  • #2
Assuming this is Earth atmosphere, atmospheric composition at sea level is ~ 80% N2 and 20% O2.
 
  • #3
I decided I have no idea what I need to do with the question at all, can anyone please help?
 

Related to Calculating Atmospheric Pressure at High Altitudes Using Quantum Mechanics

1. What is quantum/atmosphere question?

The quantum/atmosphere question refers to the relationship between quantum mechanics and the Earth's atmosphere. It explores how the principles of quantum mechanics, which govern the behavior of particles at a microscopic level, may also have an impact on the behavior of larger, more complex systems like the Earth's atmosphere.

2. How does quantum mechanics relate to the Earth's atmosphere?

Quantum mechanics is a fundamental theory that describes the behavior of particles at a microscopic level. It has been successfully applied to understand and predict the behavior of atoms and molecules. In recent years, scientists have begun to explore how these principles may also play a role in larger systems like the Earth's atmosphere, particularly in understanding weather patterns and climate change.

3. What are some examples of the quantum/atmosphere question in action?

One example is the phenomenon of quantum tunneling in the Earth's atmosphere, where particles can pass through barriers that would normally be impenetrable. This has been observed in atmospheric reactions, such as the formation of ozone. Another example is the role of quantum entanglement in atmospheric processes, where particles can become correlated and influence each other's behavior over large distances.

4. What are the implications of the quantum/atmosphere question?

The implications of the quantum/atmosphere question are still being explored, but it has the potential to deepen our understanding of atmospheric processes and improve our ability to predict and mitigate the impacts of climate change. It may also lead to new technologies and applications, such as more accurate weather forecasting models.

5. What are the challenges in studying the quantum/atmosphere question?

One of the main challenges is the complexity of the Earth's atmosphere, which involves a vast number of interacting particles and processes. This makes it difficult to isolate and study the effects of quantum mechanics in a controlled environment. Additionally, there is still much we do not know about quantum mechanics itself, so applying it to atmospheric systems requires a deep understanding of both fields.

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