# Homework Help: Atmospheric pressure and density.

1. Jun 5, 2006

### Brewer

My question states:

Given that the ground-level pressure of the Earth’s atmosphere is $$1.033 *10^5 N m^−^2,$$ calculate the mass of the atmosphere. If the ground-level atmospheric density is $$1.293 kg m^−^3$$, calculate the scale height.

For the first bit, I used P=nKT, assuming a temperature of 300K, and I then calculated the number of molecules per unit area, and multiplied this number by the surface area of the Earth. I then assumed that the atmosphere was made entirely of Nitrogen and so multiplied the number of molecules by the mass of a molecule. I ended up with the answer $$5.99*10^1^4$$ kg. Does this sound about right?

For the second part I am totally stumped. Surely if you put the height in as 0, that will tell you nothing about the scale height.

2. Jun 5, 2006

### Hootenanny

Staff Emeritus
Apparently, the total mass of the atmosphere is around 5.3x1018 kilograms according to http://hypertextbook.com/facts/1999/LouiseLiu.shtml" [Broken]. You may want to factor in oxygen as a fifth is a significant proportion. Also, try taking the earths median temperature (which is about 250k)

The scale height is defined as being The height in the atmosphere where pressure is e-1 times its value at the surface, perhaps http://scienceworld.wolfram.com/physics/PressureScaleHeight.html" [Broken] can be of some help.

Last edited by a moderator: May 2, 2017
3. Jun 5, 2006

### Brewer

They still don't give me the required order of magnitude. This is going to be a very hard exam tomorrow.

4. Jun 5, 2006

### Hootenanny

Staff Emeritus
I've just noticed something;

I hope you mean pV = nkT

5. Jun 5, 2006

### Hootenanny

Staff Emeritus
Although, accoring to Wiki (I hesitate to use this a source);