Question

Assuming that the temperature at the surface of the sun is 6000 K, find out the size of a virtual star (in terms of the size of the sun) whose surface termperature is 3000 K and the power radiated by the virtual star is 25 times the power radiated by the sun. Treat both the sun and virtual star as a blackbody.

Answer 1

Given: T_sum = 6000 k, T_star = 3000 K,

P_star = 25 × P_sun

Power radiated by the sun,

`P_(sun) = ((dQ)/dt)_(sun)`

`= σ A_(sun) T_(sun)^4 = σ 4pir_(sun)^2 T_(sun)^4`

Power radiated by the virtual star,

`P_"star" = ((dQ)/dt)_"star"`

`= σ A_"star" T_"star"^4 = σ 4pir_"star"^2 T_"star"^4`

∴ `P_"star"/P_(sun) = (σ4 pir_"star"^2T_"star"^4)/(σ4pir_(sun)^2T_(sun)^4)`

∴ `25 =( r_"star"^2 (3000)^4)/(r_(sun)^2(6000)^4)`

∴ `r_"star"^2/r_(sun)^2 = 25 xx ((6000)^4)/(3000)^4 = 400`

or `r_"star" = 20 xx r_(sun)`