Chapter 18, Problem 18.74P

Planetary Atmospheres. (a) The temperature near the top of Jupiter’s multicolored cloud layer is about 140 K. The temperature at the top of the earth’s troposphere, at an altitude of about 20 km. is about 220 K. Calculate the rms speed of hydrogen molecules in both these environments. Give your answers in m/s and as a fraction of the escape speed from the respective planet (see Problem 18.72). (b) Hydrogen gas (H₂) is a rare element in the earth’s atmosphere. In the atmosphere of Jupiter, by contrast, 89% of all molecules are H₂. Explain why, using your results from part (a). (c) Suppose an astronomer claims to have discovered an oxygen (O₂) atmosphere on the asteroid Ceres. How likely is this? Ceres has a mass equal to 0.014 times the mass of the moon, a density of 2400 kg/m³, and a surface temperature of about 200 K.