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 (H 2 ) is a rare element in the earth’s atmosphere. In the atmosphere of Jupiter, by contrast, 89% of all molecules are H 2 . Explain why, using your results from part (a). (c) Suppose an astronomer claims to have discovered an oxygen (O 2 ) 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/m 3 , and a surface temperature of about 200 K.
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 (H 2 ) is a rare element in the earth’s atmosphere. In the atmosphere of Jupiter, by contrast, 89% of all molecules are H 2 . Explain why, using your results from part (a). (c) Suppose an astronomer claims to have discovered an oxygen (O 2 ) 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/m 3 , and a surface temperature of about 200 K.
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.
The figure (Figure 1) shows representations of six
thermodynamic states of the same ideal gas sample.
Figure
1 of 1
Part A
■Review | Constants
Rank the states on the basis of the pressure of the gas sample at each state.
Rank pressure from highest to lowest. To rank items as equivalent, overlap them.
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Part A
m
2πkT
) 3/2
Calculate the integral (v) = f vƒ (v)dv. The function f(v) describing the actual distribution of molecular speeds is called the Maxwell-Boltzmann distribution,
=
ƒ(v) = 4π (· v²e-mv²/2kT
. (Hint: Make the change of variable v² =x and use the tabulated integral foxne
integer and a is a positive constant.)
Express your answer in terms of the variables T, m, and appropriate constants.
-ax dx
n!
-
an+1
where n is a positive
(v)
=
ΕΠΙ ΑΣΦ
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