The Sun has an effective temperature of 5800 K and radiates a thermal spectrum.

Question

The Sun has an effective temperature of 5800 K and radiates a thermal spectrum. The brightest star in our sky, Sirius, has an effective temperature of 9600 K and it is 1.6 times the diameter of the Sun. (a) What is the wavelength of peak brightness for the Sun and for Sirius? (Express your answer in nanometers (10^-9 m).) (b) Assuming the Sun and Sirius have the same emissivity, what is the ratio of the power of radiation produced by Sirius to that produced by the Sun? (That is, if Sirius produces twice as much radiative power, the answer would be 2.)

Explanation / Answer

a) use Wein's displacement law

lamda_m*T = k

lamda_m = k/T

= 2.898*10^-3/5800

= 5*10^-7 m

= 500 nm <<<<-----------Answer

b) according to Stefan's law power radiated by a hot body = sigma*T^4

so,

P_syrus/P_sun = (9600/5800)^4

P_syrus = P_sun*(9600/5800)^4

= 7.5*P_sun <<<<-----------Answer

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