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.

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.)

From the van der Waals equation of state, show that the critical temperature and pressure are given by T_cr = 8a / 27bR , P_cr = a / 27b². [Hint: Use the fact that the P versus V curve has an inflection point at the critical point so that the first and second derivatives are zero.]

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.)

Using the ideal gas law, find an expression for the mean free path ℓ_M that involves pressure and temperature instead of (N/V). Use this expression to find the mean free path for nitrogen molecules at a pressure of 7.5 atm and 300 K.

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%.