Question

Consider a main sequence star with a mass of 17 solar masses star with a radius of 7.6 solar

radii.

What are the following of this star:

a) luminosity?

b) surface temperature?

c) mean density?

d) average internal temperature?

e) average internal pressure?

** all work must be shown for full points

Answer 1

a) L/L(Sun) = {M/M(Sun)}ⁿ

For intermediate-to-high masses of 0.5 M(Sun) < M < 20 M(Sun), the exponent n @ 3.5.

So L/L(Sun) = (17) ^3.5 = 20256.81

L = 20256.81 Solar Luminosity

b) L₂/L₁ = (R₂/R₁)² (T₂/T₁)⁴.

L = Luminosity

R = Radius

T = Temperature

(T₂/T₁)^{4 =} 20256.81/ (7.6)^2

(T₂/T₁)^{4 =} 350.70

(T₂/T₁) = 4.33

T_{2 = 4.33 Times sun temperature.}

c) Mean density = Mass / Volume = (M/M(Sun))*(Rsun/R₁)³

Mean density = 17/(7.6)^3 = 0.0387

d) (T₂) = (10^7)*{M/M(Sun)}^1.33

(T₂) = 43 * 10^7

e) P/k = nT

(P₂/P₁) = (T₂/T₁) = 4.33