The sun,acting as a black body,emits maximum | vedclass

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(A) Given: $\lambda_m = 0.48 \ \mu m = 0.48 	imes 10^{-6} \ m$,$r = 6.96 	imes 10^8 \ m$,$\sigma = 5.67 	imes 10^{-8} \ W/m^2K^4$,$b = 0.293 	imes

Vedclass · Accepted Answer

$5.3 	imes 10^{9}$

Vedclass · Answer

(A) Given: $\lambda_m = 0.48 \ \mu m = 0.48 	imes 10^{-6} \ m$,$r = 6.96 	imes 10^8 \ m$,$\sigma = 5.67 	imes 10^{-8} \ W/m^2K^4$,$b = 0.293 	imes 10^{-2} \ m \cdot K$.$1$. Calculate the temperature of the sun using Wien's displacement law: $T = \frac{b}{\lambda_m} = \frac{0.293 	imes 10^{-2}}{0.48 	imes 10^{-6}} \approx 6104 \ K$.$2$. Calculate the surface area of the sun: $A = 4\pi r^2 = 4 	imes 3.1416 	imes (6.96 	imes 10^8)^2 \approx 6.084 	imes 10^{18} \ m^2$.$3$. Calculate the power (energy per second) radiated by the sun using Stefan-Boltzmann law: $P = A \sigma T^4 = (6.084 	imes 10^{18}) 	imes (5.67 	imes 10^{-8}) 	imes (6104)^4 \approx 4.789 	imes 10^{26} \ J/s$.$4$. Calculate the mass loss per second using Einstein's mass-energy equivalence: $\Delta m = \frac{P}{c^2} = \frac{4.789 	imes 10^{26}}{(3 	imes 10^8)^2} \approx 5.32 	imes 10^9 \ kg/s$.

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