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Matter inside a ''white dwarf'' is in a state of degeneracy, and the dependence of the pressure on the density is of the form P=Arho^(5//3), where P is the pressure and rho is the density. Find the expression for the constant A and show that the pressure is due to the electron gas, the pressure due to the heavy particles being negligible. |
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Answer» `PV^(5//3)=H^(2)/(5m_(e))(3/(8pi))^(2//3)N_(e)^(5//3)` There are two electrons to each helium nucleus, so `N_(e)=2N_(alpha)=2M//m_(alpha)` where M is the mass of the star, and `m_(alpha)=4.002xx1.66xx10^(-27)kg` is the mass of a helium nucleus. Hence `PV^(5//3)=AM^(5//3),orP=Arho^(5//3)`, where `A=h^(2)/(5m_(e)(m_(alpha)//2)^(5//3))(3/(8pi))^(2//3)=3.2xx10^(5)Pa*m^(5)*kg^(5//3)` |
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