Thickness of Earth's atmosphere

[elliotyang]

Homework Statement

Calculate the thickness of Earth's atmosphere.
Assume that the pressure and temperature do not vary with height.
Make reasonable assumptions for their values.

Homework Equations

I think this question has to be solve with ideal gas equation which is PV=nRT

The Attempt at a Solution

Since the problem stated that the pressure and temperature do not vary with height,
so I assume it is stp which pressure is 1atm, and 25^。c (I suppose the absolute temperature for ideal gas law to be 273 K, but it seems to be impractical and not consistent with the problem).
then i stuck, i do not know how to obtain the value for n.

 

[Valkarie]

or should i simply use the equation P=ρgh,where h is the thickness of atmosphere i want to obtain, and g is 9.8 m/s2,and ρ is density of air, which refer to the table, at 25。C, pressure is 1atm, the density is 1.2kg/m3.then we get h=P/ρg = 1/(1.2*9.8) = 0.08163 m.Is it okay?

 

[Mene]

To calculate the thickness of Earth's atmosphere, we can use the ideal gas law as you have suggested. However, it is important to note that the atmosphere is not comprised of a single gas, so we cannot simply use the ideal gas law with one value for n. Instead, we can use the ideal gas law for each individual gas present in the atmosphere and then add them together to get the total thickness.

To do this, we need to make some reasonable assumptions about the composition of the atmosphere. The Earth's atmosphere is primarily made up of nitrogen (78%) and oxygen (21%), with small amounts of other gases such as carbon dioxide, water vapor, and argon. We can assume that the rest of the gases present make up the remaining 1% of the atmosphere.

Using the ideal gas law, we can calculate the thickness of each gas layer by solving for the height (h) in the following equation:

h = (nRT)/P

Where n is the number of moles of gas, R is the ideal gas constant, T is the temperature in Kelvin, and P is the pressure in atmospheres.

For nitrogen, we can assume that the pressure is 1 atm and the temperature is 25°C (298 K). Using the molar mass of nitrogen (28 g/mol), we can calculate the number of moles of nitrogen in the atmosphere (78% of 5.148 x 10^18 kg, the total mass of the atmosphere):

n = (0.78 x 5.148 x 10^18 kg) / (28 g/mol) = 1.418 x 10^20 mol

Plugging this value into the equation, we get a thickness of approximately 800 km for the nitrogen layer.

We can repeat this process for oxygen, assuming the same pressure and temperature, and using the molar mass of oxygen (32 g/mol). This gives us a thickness of approximately 550 km for the oxygen layer.

For the remaining gases, we can assume that they make up 1% of the atmosphere, so we can use the same pressure and temperature and calculate the thickness as a percentage of the total thickness. This gives us a thickness of approximately 6 km for the remaining gases layer.

Adding all of these values together, we get a total thickness of approximately 1356 km for Earth's atmosphere. Keep in mind that this is just an estimate and there may be variations in the actual thickness due to factors