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?

(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

(a) 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. (

(b) Determine the number of collisions a single Cs atom undergoes with other cesium atoms per second.

(III) Starting from the Maxwell distribution of speeds, Eq. 18–6, show

(a) ∫₀∞ ƒ(v)dv = N, which is the total number of molecules, and

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 vᵣₘₛ (at 20°C) for water molecules is this? (Assume Eq. 18–4 holds.)

(II) 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:

(a) Determine vᵣₘₛ for this distribution of speeds.

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