Astronomers have recently discovered a new planet in a faraway solar system with a radius of roughly 395 km.395 km. Spectroscopic results indicate that the atmosphere, whose height is much smaller than the planet's radius, is largely argon, making the discovery truly controversial. Experts have deduced that argon is unlikely to be generated from the planet itself, therefore it is assumed that the argon in the atmosphere was created at the inception of the planet and is completely contained by its gravitational attraction. However, wide disagreement abounds about the composition of the planet. The surface of the planet is clearly composed of aluminum oxide, but some astronomers claim that this aluminum oxide is only a thin crust and that the planet is mostly iron. Given that the atmospheric temperature is 512 ∘C,512 ∘C, calculate the minimum density ?ρ of the planet so that its atmosphere could contain argon atoms. The molar mass of argon is 39.948 g/mol39.948 g/mol and the gravitational constant is 6.670×10−11 m3/(kg⋅s2).6.670×10−11 m3/(kg⋅s2). Avogradro's number is 6.022×1023 mol−16.022×1023 mol−1 and the Boltzmann constant is 1.380×10−23 J/K.
Astronomers have recently discovered a new planet in a faraway solar system with a radius of roughly 395 km.395 km. Spectroscopic results indicate that the atmosphere, whose height is much smaller than the planet's radius, is largely argon, making the discovery truly controversial. Experts have deduced that argon is unlikely to be generated from the planet itself, therefore it is assumed that the argon in the atmosphere was created at the inception of the planet and is completely contained by its gravitational attraction. However, wide disagreement abounds about the composition of the planet. The surface of the planet is clearly composed of aluminum oxide, but some astronomers claim that this aluminum oxide is only a thin crust and that the planet is mostly iron. Given that the atmospheric temperature is 512 ∘C,512 ∘C, calculate the minimum density ?ρ of the planet so that its atmosphere could contain argon atoms. The molar mass of argon is 39.948 g/mol39.948 g/mol and the gravitational constant is 6.670×10−11 m3/(kg⋅s2).6.670×10−11 m3/(kg⋅s2). Avogradro's number is 6.022×1023 mol−16.022×1023 mol−1 and the Boltzmann constant is 1.380×10−23 J/K.
Modern Physics
3rd Edition
ISBN:9781111794378
Author:Raymond A. Serway, Clement J. Moses, Curt A. Moyer
Publisher:Raymond A. Serway, Clement J. Moses, Curt A. Moyer
Chapter10: Statistical Physics
Section: Chapter Questions
Problem 6P
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Astronomers have recently discovered a new planet in a faraway solar system with a radius of roughly 395 km.395 km. Spectroscopic results indicate that the atmosphere, whose height is much smaller than the planet's radius, is largely argon, making the discovery truly controversial. Experts have deduced that argon is unlikely to be generated from the planet itself, therefore it is assumed that the argon in the atmosphere was created at the inception of the planet and is completely contained by its gravitational attraction.
However, wide disagreement abounds about the composition of the planet. The surface of the planet is clearly composed of aluminum oxide, but some astronomers claim that this aluminum oxide is only a thin crust and that the planet is mostly iron.
Given that the atmospheric temperature is 512 ∘C,512 ∘C, calculate the minimum density ?ρ of the planet so that its atmosphere could contain argon atoms. The molar mass of argon is 39.948 g/mol39.948 g/mol and the gravitational constant is 6.670×10−11 m3/(kg⋅s2).6.670×10−11 m3/(kg⋅s2). Avogradro's number is 6.022×1023 mol−16.022×1023 mol−1 and the Boltzmann constant is 1.380×10−23 J/K.
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