Atmospheric pressure and density.

[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.

 

[Hootenanny]

Apparently, the total mass of the atmosphere is around 5.3x10¹⁸ kilograms according to http://hypertextbook.com/facts/1999/LouiseLiu.shtml" . You may want to factor in oxygen as a fifth is a significant proportion. Also, try taking the Earth's 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" can be of some help.

 

[Brewer]

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

 

[Hootenanny]

I've just noticed something;

For the first bit, I used P=nKT

I hope you mean pV = nkT

 

[Hootenanny]

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

According to the National Center for Atmospheric Research, "The total mean mass of the atmosphere is 5.1480 x 10^18 kg with an annual range due to water vapor of 1.2 or 1.5 x 10^15 kg depending on whether surface pressure or water vapor data are used; somewhat smaller than the previous estimate. The mean mass of water vapor is estimated as 1.27 x 10^16 kg and the dry air mass as 5.1352 ±0.0003 x 10^18 kg."