Question

u(λ,T)=4E(λ,T)/c

2. Use the energy density expression above and the Stefan-Boltzmann expression, u(T) 014 with σ= 7.56x 10.15 erg/cmK4, to obtain a formula for the total rate of radiation per unit area of a black body. Assume that the sun radiates as a black body. You are given the radius of the sun R -7x101° cm, the average distance of the sun to the earth d Lx10 c, nthe solar consdant, the aount of enexgy : carth when the sun is overhead 1.4x10° erg/cm'sec. Use this information to estimate the surface temperature of the sun. (10 points)

Answer 1

For surface tem of sum rho = sigma T^4 We know power = 1.4 times 10^6 times (4 pi R^2) = 1.4 times 10^6 times 4 times 3.14 times (7 times 10^10)^2 = 8.616 times 10^28 erg/sec and P = sigma T^4 p/sigma = T^4 T = [p/sigma]^1/4 T = [8.616 times 10^28 erg/sec/7.56 times 10^-15 erg/cm^3]^1/4 T = [1.139 times 10^43]^1/4 T = 5.810 times 10^10 K