Physics

Physics · modern-physics

Problem

A.1 Assume that the Sun radiates like a perfect blackbody. Use this fact to calculate the temperature, TsT_{\mathrm{s}}, of the solar surface. Given constants: Particles from the Sun 1{ }^{1} Photons from the surface of the Sun and neutrinos from its core can tell us about solar temperatures and also confirm that the Sun shines because of nuclear reactions. Throughout this problem, take the mass of the Sun to be M⊙=2.00×1030 kgM_{\odot}=2.00 \times 10^{30} \mathrm{~kg}, its radius, R⊙=7.00×R_{\odot}=7.00 \times 108 m10^{8} \mathrm{~m}, its luminosity (radiation energy emitted per unit time), L⊙=3.85×1026 WL_{\odot}=3.85 \times 10^{26} \mathrm{~W}, and the Earth-Sun distance, d⊙=1.50×1011 md_{\odot}=1.50 \times 10^{11} \mathrm{~m}. Note: (i) ∫xeaxdx=(xa−1a2)eax+\int x e^{a x} d x=\left(\frac{x}{a}-\frac{1}{a^{2}}\right) e^{a x}+ constant (ii) ∫x2eaxdx=(x2a−2xa2+2a3)eax+\int x^{2} e^{a x} d x=\left(\frac{x^{2}}{a}-\frac{2 x}{a^{2}}+\frac{2}{a^{3}}\right) e^{a x}+ constant (iii) ∫x3eaxdx=(x3a−3x2a2+6xa3−6a4)eax+\int x^{3} e^{a x} d x=\left(\frac{x^{3}}{a}-\frac{3 x^{2}}{a^{2}}+\frac{6 x}{a^{3}}-\frac{6}{a^{4}}\right) e^{a x}+ constant A Radiation from the sun :

Browse the problem library