The star (u) Cephei, sometimes known as \"Herschel\'s Garnet Star\" is a red sup

Question

The star (u) Cephei, sometimes known as "Herschel's Garnet Star" is a red supergiant start that has the distinction of being one of the largest stars known. As might be expected, its surface temperature is much cooler than the sun, probably close to 3150 K (about the temperature of a light bulb filament; hence its perceived "redness"). Its luminosity (total radiated power) is 1.18 X 1032 W.

a) Using the Stefan-Boltzmann radiation law and assuming that it radiates like a black body (emissivity = 1), find its radius.

b) By comparison, the radius of the Sun is 6.96 X 108 m. How many times greater than the Sun's radius is the radius of (u) Cephei?

Explanation / Answer

a)

rate of energy radiation is,

power=E/t=sigma*e*A*T^4

here

emissivity e=1

stefan constant sigma=5.67*10^-8 W*m^2/K4

Area A=4pi*R^2

now

power=E/t=sigma*A*T^4

1.18*10^32=5.67*10^-8*4pi*R^2*3150^4

R^2=1.18*10^32/5.67*10^-8*4pi*3150^4

R^2=1.6829*10^24

===>

radius of star Rstar=1.29726*10^12 m ............

b)

radius of sun is R_sun=6.96*10^8 m

and

R_star=1.29726*10^12 m

or

R_star/R_sun=1.29726*10^12/6.96*10^8

R_star/R_sun=1863.88

R_star=1863.88*R_sun ...............

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