Astronomers have recently discovered a new planet in a faraway solar system with a radius of roughly 1211 km. Spectroscopic results indicate that the atmosphere, whose height is much smaller than the planet's radius, is largely helium, making the discovery truly controversial. Experts have deduced that helium is unlikely to be generated from the planet itself, therefore it is assumed that the helium 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 562 ∘C, calculate the minimum density ? of the planet so that its atmosphere could contain helium atoms. The molar mass of helium is 4.002 g/mol and the gravitational constant is 6.670×10−11 m3/(kg⋅s2). Avogradro's number is 6.022×10^23 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 1211 km. Spectroscopic results indicate that the atmosphere, whose height is much smaller than the planet's radius, is largely helium, making the discovery truly controversial. Experts have deduced that helium is unlikely to be generated from the planet itself, therefore it is assumed that the helium 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 562 ∘C, calculate the minimum density ? of the planet so that its atmosphere could contain helium atoms. The molar mass of helium is 4.002 g/mol and the gravitational constant is 6.670×10−11 m3/(kg⋅s2). Avogradro's number is 6.022×10^23 mol−1 and the Boltzmann constant is 1.380×10−23 J/K.
College Physics
11th Edition
ISBN:9781305952300
Author:Raymond A. Serway, Chris Vuille
Publisher:Raymond A. Serway, Chris Vuille
Chapter10: Thermal Physics
Section: Chapter Questions
Problem 57AP
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Astronomers have recently discovered a new planet in a faraway solar system with a radius of roughly 1211 km. Spectroscopic results indicate that the atmosphere, whose height is much smaller than the planet's radius, is largely helium, making the discovery truly controversial. Experts have deduced that helium is unlikely to be generated from the planet itself, therefore it is assumed that the helium 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 562 ∘C, calculate the minimum density ? of the planet so that its atmosphere could contain helium atoms. The molar mass of helium is 4.002 g/mol and the gravitational constant is 6.670×10−11 m3/(kg⋅s2). Avogradro's number is 6.022×10^23 mol−1 and the Boltzmann constant is 1.380×10−23 J/K.
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