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Planetary Atmospheres. (a) The temperature near the top of
Chapter 18, Problem 78P(choose chapter or problem)
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 and as a fraction of the escape speed from the respective planet (see Problem 18.76). (b) Hydrogen gas \(\left(\mathrm{H}_{2}\right)\) is a rare element in the earth’s atmosphere. In the atmosphere of Jupiter, by contrast, 89% of all molecules are \(\mathrm{H}_{2}\). Explain why, using your results from part (a). (c) Suppose an astronomer claims to have discovered an oxygen \( \(\left(\mathrm{O}_{2}\right)\)\) 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 \(2400 \mathrm{kg} / \mathrm{m}^{3}\) and a surface temperature of about 200 K.
Questions & Answers
QUESTION:
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 and as a fraction of the escape speed from the respective planet (see Problem 18.76). (b) Hydrogen gas \(\left(\mathrm{H}_{2}\right)\) is a rare element in the earth’s atmosphere. In the atmosphere of Jupiter, by contrast, 89% of all molecules are \(\mathrm{H}_{2}\). Explain why, using your results from part (a). (c) Suppose an astronomer claims to have discovered an oxygen \( \(\left(\mathrm{O}_{2}\right)\)\) 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 \(2400 \mathrm{kg} / \mathrm{m}^{3}\) and a surface temperature of about 200 K.
ANSWER:Solution 78P Problem (a) Rms speed of Hydrogen molecule at the top of Jupiter and Earth Step 1: At Jupiter T = 140K Mass of single Hydrogen atom = 1.67x10 27kg Mass of Hydrogen molecule m = 2 x 1.67x10 27kg k = 1.381x10 23J/K