Question

In: Mechanical Engineering

Sirius has a mass of 2 solar masses and radius of 1.71 solar radius, determine average...

Sirius has a mass of 2 solar masses and radius of 1.71 solar radius, determine average
density of Sirius.

a) pressure at half radius of Sirius b) temperature at half radius of Sirius c) radiation pressure at half radius.

Hint: You may find the ideal gas law helpful. Mean molecular weight for outer layers of stars is ~ 0.61.

Expert Solution

Mass of sun = 1.988 x 10³⁰. kg

2 solar mass = 2 * 1.988x 10³⁰ kg mass of sirius.

Radius of sirius = 1.7 * 696340 km = 1183778 km

Volume of Sirius = 4/3 r³. = 6.95×10¹⁸ Km³.

Density = mass / volume = 3.976x10³⁰ / 6.95×10¹⁸ = 5.721 x 10¹¹ kg/km³.

Density of sirius = 5.721 x 10¹¹ kg/km³.

Pressure = g².

g = M/ r².

P central = g central².

ghalf = Mass half / radius half².

Half radius = 1183778/2 =591889 km

= 1.988 x 10³⁰. / 591889 = 5.675 x 10¹⁸.

Pressure = ghalf ² = 3.22x10³⁷kg/km².

Ideal gas equation

PV = nRT

Volume = 4/3 (r/2)³. = 8.69×10¹⁷

(3.22x10³⁷ * 8.69×10¹⁷ ) = 0.61 * 287.058 * T

T = (3.22x10³⁷ * 8.69×10¹⁷ ) / 0.61 * 287.058 = 1.6 x 10⁵³K.

Considering a perfect reflection raidatio

Radiation pressure Prad = Pressure * 2 = 2 *3.22x10³⁷kg/km². = 3.22 x 10⁷⁴.kg/km².

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