Gas Distribution Homework: Calculating Particle Mass to Escape Planet's Gravity

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Homework Help Overview

The problem involves calculating the mass of gas particles that can escape a planet's gravitational pull, given the planet's mass, radius, and the temperature of the gas. The context is rooted in concepts from thermodynamics and gravitational physics.

Discussion Character

  • Exploratory, Conceptual clarification, Mathematical reasoning

Approaches and Questions Raised

  • Participants discuss the relationship between escape velocity and particle mass, with some attempting to connect the Maxwell-Boltzmann distribution to the problem. Questions arise regarding the correct application of formulas and the interpretation of the hint provided.

Discussion Status

Some participants have expressed confusion about the problem, while others have suggested potential approaches and formulas to consider. There is an indication of varying interpretations of the problem, and some guidance has been offered regarding the use of escape velocity.

Contextual Notes

Participants note the use of the average velocity and the implications of the Maxwell-Boltzmann distribution, while also grappling with the definitions and relationships between the variables involved.

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Homework Statement



A planet has mass, 2 x 1022 kg, and radius, 2 x 106 m. Initially, its
atmosphere contains gas particles of various masses. If the gas is at temperature, 400 K,
and has a Maxwell-Boltzmann velocity distribution, what mass of particle will typically
escape from the planet’s gravitational pull? (Hint: You can just use the average velocity,
you don’t need to consider the full Maxwell-Boltzmann distribution).

Homework Equations


vrms=sqrt(3kbT/m)
P(v)=v^2*e^(-0.5mv^2/kbT)


The Attempt at a Solution



I have no clue at all
Please help me
 
Physics news on Phys.org
wait i got it.. thx
the vrms was the escape velocity
hahaha XD
 
Im having problems with this problem too can you tell me how you got it?
 
escape velocity v=sqrt2GM/ R
you need to use this velocity for maxwell-boltzmann speed distribution:
2GM/r= 3kT/m
you can find m from here.
I hope that helps:))
 

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