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Pressure inside the sphere

  • Thread starter 78141471
  • Start date
  • #1
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Homework Statement



I have a sphere filled with unknown gas. I have to estimate the pressure inside of it.

  • The tricky part is that density of the sphere changes as we go deeper inside of it with the given formula:
    ρ=ρo*(1-r/R), where R is radius of the sphere and is known: R=5*1010m, and r is a variable.
  • Gas has mol mass m=2.7 g/mol.
  • Mass of the whole sphere is M=3.3*1050 kg.
  • Gas is ideal.

Homework Equations



  • pV=nRT
  • p=F/A


The Attempt at a Solution



The force of gravity of an infinitesimal layer of thickness dr inside the sphere at some radius r caused by the inner sphere is:

dF=GmM/r2 where m is the mass of the infinitesimal layer and M is the mass of inner part of the sphere.

Mass m=V*ρ=4*PI*r2o*(1-r/R)*dr
Mass M=4/3*PI*r3o*(1-r/R)

so dF=G*16/3*PI2*r3o2*(1-r/R)2*dr

dp=dF/A
dp=dF/4*PI*r2
dp=4/3*PI*G*ρo2*(1-r/R)2*r*dr

so
p(r)=4/3*PI*G*ρo2*[tex]\int[/tex](1-r/R)2*r*dr from r to R

After making the calculations I will put p(r=0) and get the pressure inside the sphere. Is my method good?
 

Answers and Replies

  • #2
2
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too hard or did I do something wrong?
 

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