The escape speed from the Earth is 1.12 x 10⁴ m/s (Section 8–7). So a gas molecule traveling away from Earth near the outer boundary of the Earth’s atmosphere would, at this speed, be able to escape from the Earth’s gravitational field and be lost to the atmosphere. Can you explain why our atmosphere contains oxygen but not helium?

The escape speed from the Earth is 1.12 x 10⁴ m/s (Section 8–7). So a gas molecule traveling away from Earth near the outer boundary of the Earth’s atmosphere would, at this speed, be able to escape from the Earth’s gravitational field and be lost to the atmosphere. At what temperature is the rms speed of oxygen molecules?

For an ideal gas at temperature T show that$\frac{d{v}_{rms}}{dT}=\frac{1}{2}\left(\frac{v_{rms}}{T}\right)$, and using the approximation $\Delta v_{rms}\approx \left(\frac{d{v}_{rms}}{dT}\right)\Delta T$, show that $\frac{\Delta v_{rms}}{v_{rms}}\approx \frac{1}{2}\left(\frac{\Delta T}{T}\right)$.

Calculate the total water vapor pressure in the air on the following day: a hot summer day, with the temperature 30°C and the relative humidity at 75%.

A space vehicle returning from the Moon enters the Earth’s atmosphere at a speed of about 42,000 km/h. Molecules (assume nitrogen) striking the nose of the vehicle with this speed correspond to what temperature? (Because of this high temperature, the nose of a space vehicle must be made of special materials; indeed, part of it does vaporize, and this is seen as a bright blaze upon reentry.)

(I) Twelve molecules have the following speeds, given in arbitrary units: 6.0, 2.0, 4.0, 6.0, 0.0, 4.0, 1.0, 8.0, 5.0, 3.0, 7.0, and 8.0. Calculate the mean speed.

What is the temperature of a sample of CO₂ molecules whose rms speed is 300 m/s? The molecular mass for Carbon and Oxygen is 12.01 g/mol and 16 g/mol, respectively.

Oxygen (O₂) has a molar mass of $32.0$ g/mol. How many oxygen molecules traveling at this speed are necessary to produce an average pressure of $1$ atm?

Oxygen (O₂) has a molar mass of $32.0$ g/mol. Suppose an oxygen molecule traveling at this speed bounces back and forth between opposite sides of a cubical vessel $0.10$ m on a side. What is the average force the molecule exerts on one of the walls of the container? (Assume that the molecule's velocity is perpendicular to the two sides that it strikes.)