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.
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.
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?