21. Kinetic Theory of Ideal Gases

The escape velocity from the Earth is approximately 11.2 km/s. If the mass of helium atoms is 6.64 × 10^-27 kg, at what temperature would the average speed of helium atoms be equal to the escape velocity?

For a gas of nitrogen molecules (N₂), what must the temperature be if $94.7\%$ of all the molecules have speeds less than $1500$ m/s? Use Table $18.2$. The molar mass of N₂ is $28.0$ g/mol.

For diatomic carbon dioxide gas (CO₂, molar mass $44.0$ g/mol) at $T = 300$ K, calculate the average speed $v_{av}$.

For diatomic carbon dioxide gas (CO₂, molar mass $44.0$ g/mol) at $T = 300$ K, calculate the most probable speed $v_{mp}$.

(II) A group of 25 particles have the following speeds: two have speed 10 m/s, seven have 15 m/s, four have 20 m/s, three have 25 m/s, six have 30 m/s, one has 35 m/s, and two have 40 m/s. Determine the average speed.