Assume that the temperature of the surface of the sun is 5000 K and the surface temperature of another virtual star is 2500 K. The power radiated by a virtual star is 30 times the power radiated by the sun. The radius of a virtual star in terms of the radius of the sun is Treat both the sun and the virtual star as a black body

Step-by-step solution

According to the Stefan-Boltzmann law, the power radiated by a black body is given by P = A T^4 = (4 r^2) T^4 . For the sun: P_ s = (4 r_ s ^2) T_ s ^4 For the virtual star: P_ v = (4 r_ v ^2) T_ v ^4 Given P_ v = 30 P_ s , we have: (4 r_ v ^2) T_ v ^4 = 30 (4 r_ s ^2) T_ s ^4 r_ v ^2 r_ s ^2 = 30 ( T_ s T_ v )^4 Substituting T_ s = 5000 K and T_ v = 2500 K: r_ v ^2 r_ s ^2 = 30 ( 5000 2500 )^4 r_ v ^2 r_ s ^2 = 30 (2)^4 = 30 16 = 480 r_ v = 480 r_ s = 4 30 r_ s Answer: 4 30 ,r_ sun