How is the popular estimate of the Earth's atmospheric mass correct?

[Dreksler]

TL;DR Summary

How is the popular estimate of the Earth's atmospheric mass correct if it is just based on the force applied per a certain surface area?

There is a number floating around on the internet that says that the mass of the Earth's atmosphere is about 5 quintillion kilograms. The way that that number was calculated was through knowing that per square meter of surface area at sea level, about 100,000 Newtons of force is applied, which then translated into kilograms per force is about 10,000 KpF, and then you just multiply that per square meter number with the Earth's surface area in meters.

Now what I am puzzled by is that since temperature affects the pressure, if for some reason the temperature suddenly dropped to about -50 degrees celsius globally, the pressure would too, meaning that a lower amount Newtons will be applied per squared meter, leading to a lower KpF number which then leads to a lower estimate of the Earth's mass through that method.

So then how is the 5 quintillion kilograms of total atmospheric mass of the Earth a correct number if the number is just based on the force applied? I am assuming that I am missing something large in my reasoning here so that is why I am asking for some clarification here on that number.

 

[A.T.]

temperature affects the pressure,

You mean in a container? Is the atmosphere enclosed in a container?

if for some reason the temperature suddenly dropped to about -50 degrees celsius globally, the pressure would too,

In desert areas the temperature drops almost that much during the night. Does this effect the atmospheric pressure substantially?

 

[Dale]

Summary:: How is the popular estimate of the Earth's atmospheric mass correct if it is just based on the force applied per a certain surface area?

Now what I am puzzled by is that since temperature affects the pressure, if for some reason the temperature suddenly dropped to about -50 degrees celsius globally, the pressure would too,

The ideal gas law is $PV= nRT$. So (with $n$ and $R$ constant) a change in $T$ implies a change in $PV$ which is not the same as a change in $P$.

 

[Chestermiller]

Does changing the temperature change the weight of a 1 m^2 column of air above the surface?

 

[DaveC426913]

Does changing the temperature change the weight of a 1 m^2 column of air above the surface?

No, but I can see his point nonetheless. Changing the temp would make it difficult to determine the pressure (average global), which is what is being used to calculate the weight.

 

[Chestermiller]

No, but I can see his point nonetheless. Changing the temp would make it difficult to determine the pressure (average global), which is what is being used to calculate the weight.

The global average pressure at the surface (sea level) is known. See the U.S. Standard Atmosphere. It comes out to what we call 1 atm. How accurately do you need it?

 

[hmmm27]

since temperature affects the pressure, if for some reason the temperature suddenly dropped to about -50 degrees celsius globally, the pressure would too, meaning that a lower amount Newtons will be applied per squared meter, leading to a lower KpF number which then leads to a lower estimate of the Earth's mass through that method.

No matter what the temperature, there's still the same mass of air, and close enough the same weight. Water vapour messes with that, somewhat.

 

[DaveC426913]

The global average pressure at the surface (sea level) is known. See the U.S. Standard Atmosphere. It comes out to what we call 1 atm. How accurately do you need it?

Ah. Right. I assumed one was measuring it locally and extrapolating.

 

[Baluncore]

So then how is the 5 quintillion kilograms of total atmospheric mass of the Earth a correct number if the number is just based on the force applied? I am assuming that I am missing something large in my reasoning here so that is why I am asking for some clarification here on that number.

Since the area of the Earth's surface does not change, and the total mass of the atmosphere does not change significantly over the measurement period, the average air pressure over the entire Earth's surface must remain constant.

If you consider thermal changes in local, regional, or global air density, then you are overthinking the elegant solution.