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.

A sample of cesium vapor is in an oven at 400°C. The volume of the oven is 75 cm³, the vapor pressure of Cs at 400°C is 17 mm-Hg, and the diameter of cesium atoms in the vapor is 0.33 nm. Determine the number of collisions a single Cs atom undergoes with other cesium atoms per second.

Starting from the Maxwell distribution of speeds, Eq. 18–6, show ${\int }_0^{\infty }f\left(v\right)dv=N,$ which is the total number of molecules.

At room temperature, it takes approximately 2.45 x 10³ J to evaporate 1.00 g of water. Estimate the average speed of evaporating molecules. What multiple of v_rms (at 20°C) for water molecules is this? (Assume Eq. 18–4 holds.)

A gas consisting of 14,500 molecules, each of mass 2.00 x 10⁻²⁶ kg, has the following distribution of speeds, which crudely mimics the Maxwell distribution. Determine vᵣₘₛ for this distribution of speeds.