- #1
Saitama
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Homework Statement
(see attachment 1)
Homework Equations
The Attempt at a Solution
(see attachment 2)
As the gas is ideal and there is no gravity, the pressure is same throughout the cloud. In the thin sphere shown, the mass of the gas is ##dm=dV \cdot \rho(r)##. Let ##\mu## be the molar mass of gas.
From ideal gas law
[tex]PV=nRT[/tex]
[tex]P(dV)=\frac{dm}{\mu}RT=\frac{dV \rho(r)}{\mu}RT[/tex]
[tex]P=\frac{\rho_0}{\mu r^2}RT[/tex]
Since ##P, \rho_0## and ##\mu## are constant, ##T## is directly proportional to ##r^2##.
This gives ##T_{r_0}/T_{2r_0}=0.25##, but this is wrong.
Any help is appreciated. Thanks!