(adsbygoogle = window.adsbygoogle || []).push({}); 1. The problem statement, all variables and given/known data

Air at sealevel is composed of 80% nitrogen and 20% oxygen, but at the top of Mount Everest the composition of air is different. Give an expression for the ratio ([itex]f_O[/itex]) of oxygen in the air as a function of height z above sealevel, assuming the temperature T is constant and the air is an ideal gas. The gravitational acceleration is g and the mass of a molecule of nitrogen is [itex]m_N[/itex] and the mass of a molecule of oxygen is [itex]m_O[/itex].

3. The attempt at a solution

The potential energy of a molecule of oxygen is [itex]m_O g z[/itex], so the probability of finding it at height z is: [itex]P_{mO}(z) \propto e^{-\frac{m_O g z}{k_B T}}[/itex]. Similarly for nitrogen: [itex]P_{mN}(z) \propto e^{-\frac{m_N g z}{k_B T}}[/itex]. So the ratio is simply [itex]f_O = \frac{e^{-\frac{m_O g z}{k_B T}}}{e^{-\frac{m_N g z}{k_B T}}} = e^{-\frac{(m_O - m_N)gz}{k_B T}}?[/itex]

**Physics Forums | Science Articles, Homework Help, Discussion**

Dismiss Notice

Join Physics Forums Today!

The friendliest, high quality science and math community on the planet! Everyone who loves science is here!

The friendliest, high quality science and math community on the planet! Everyone who loves science is here!

# Homework Help: Ratio of oxygen in atmosphere

**Physics Forums | Science Articles, Homework Help, Discussion**