a) The temperature near the top of Jupiter\'s multicolored cloud layer is about

Question

a) The temperature near the top of Jupiter's multicolored cloud layer is about 140 K. Calculate the rms speed of hydrogen molecules in this environment. Give your answer in m/s.

b) Give your answer as a fraction of the escape speed from the planet.

c) 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 this environment. Give your answer inm/s.

d) Give your answer as a fraction of the escape speed from the planet.

Explanation / Answer

I need the formula Vrms = sqrt(3RT/M)

M of H2 = 2g/mol = .002kg/mol

Vrms Jupiter = sqrt(3x8.314x140k/.002kg) = 1.321x10^3 m/s
Vrms Earth = sqrt(3x8.314x220k/.002kg)= 1.656x10^3 m/s

I suppose use the given formula (2GM/R)^1/2 to calculate each plantes escape and then divide that number by the Vrms of jupiter and Earth. But What is g, M, and R of jupiter?? Is 9.8m/s the gravitational force at 20km high in the earths atmosphere??

So, I am using some standard result which are already calculated, as the above information is not mentioned in the question.

In the case of the earth, the escape velocity is 11.2kps/6.9mps and Jupiter, 59.6kps/37mps.

a)) Vrms Jupiter = sqrt(3x8.314x140k/.002kg) = 1.321x10^3 m/s

b)) = (1.321x10^3 m/s) /37 m/s = 35.702 m/s

c)) Vrms Earth = sqrt(3x8.314x220k/.002kg)= 1.656x10^3 m/s

d)) = (1.656x10^3 m/s) / 6.9 m/s = 240 m/s

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