Atmosphere model approximation limits

[mumaga]

I am modelling the atmosphere as a perfect, static gas subject to uniform gravity, assuming ideal gas equation, the density is found to follow: p=A*exp(-z/H) where A is a const, z is the heigh, and L is the scale height.

I want to know when this approximation breaks down! at what density? i am thinking that as the density goes down the approximation for he idea gas law breaks, but not quite sure if there is a specific value at which it breaks! maybe a certain number of molecules??

thanks a million!

 

[Chestermiller]

I am modelling the atmosphere as a perfect, static gas subject to uniform gravity, assuming ideal gas equation, the density is found to follow: p=A*exp(-z/H) where A is a const, z is the heigh, and L is the scale height.

I want to know when this approximation breaks down! at what density? i am thinking that as the density goes down the approximation for he idea gas law breaks, but not quite sure if there is a specific value at which it breaks! maybe a certain number of molecules??

thanks a million!

Are you asking (a) What are the limitations of the ideal gas law? or (b) What are the limitations of the atmospheric density equation?

I will address the second question. The equation you gave assumes that the temperature of the atmosphere is independent of altitude, such that the scale height is a constant. If you take into account the fact that the temperature varies, then the exponential term contains an integral, and the parameter A is temperature dependent.

 

[mumaga]

Thank Chestermiller!

The thing is that the questions asks at which density the approximation breaks and consequently at what height, i was thinking maybe that would happen at the stratosphere, as the temperature starts to increase in their due to the absorption of UV, so above 9km!