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6. Using the integral ??? (x³ / (e? - 1)) dx = ?? / 15, deduce the expression for the constant of proportionality a. 7. The power emitted per unit of area for a black body is given by the Stefan-Boltzmann law R = (c / 4) U = ?T?, where c is the speed of light and ? is Stefan’s constant. Determine ? and calculate its numerical value. 8. The temperature at the surface of the Sun is approximately 5800 K. What is its power emitted per unit of area? 9. The Sun’s radius is 6.96 × 10? m. What is the total power radiated by the Sun? 10. The energy of the Sun originates mainly from the conversion of hydrogen to helium, and the creation of each helium nucleus from four protons releases 26.7 MeV of energy, mainly in the form of radiation. What mass of hydrogen is transformed every second? Compared with the mass of the Sun equal to 1.99 × 10³? kg, what fraction of the Sun’s mass disappears every second?

          6. Using the integral
??? (x³ / (e? - 1)) dx = ?? / 15,
deduce the expression for the constant of proportionality a.
7. The power emitted per unit of area for a black body is given by the Stefan-Boltzmann law
R = (c / 4) U = ?T?,
where c is the speed of light and ? is Stefan’s constant. Determine ? and calculate its numerical value.
8. The temperature at the surface of the Sun is approximately 5800 K. What is its power emitted per unit of area?
9. The Sun’s radius is 6.96 × 10? m. What is the total power radiated by the Sun?
10. The energy of the Sun originates mainly from the conversion of hydrogen to helium, and the creation of each helium nucleus from four protons releases 26.7 MeV of energy, mainly in the form of radiation. What mass of hydrogen is transformed every second? Compared with the mass of the Sun equal to 1.99 × 10³? kg, what fraction of the Sun’s mass disappears every second?

$6. Using the integral ??? (x³ / (e? - 1)) dx = ?? / 15, deduce the expression for the constant of proportionality a. 7. The power emitted per unit of area for a black body is given by the Stefan-Boltzmann law R = (c / 4) U = ?T?, where c is the speed of light and ? is Stefan’s constant. Determine ? and calculate its numerical value. 8. The temperature at the surface of the Sun is approximately 5800 K. What is its power emitted per unit of area? 9. The Sun’s radius is 6.96 × 10? m. What is the total power radiated by the Sun? 10. The energy of the Sun originates mainly from the conversion of hydrogen to helium, and the creation of each helium nucleus from four protons releases 26.7 MeV of energy, mainly in the form of radiation. What mass of hydrogen is transformed every second? Compared with the mass of the Sun equal to 1.99 × 10³? kg, what fraction of the Sun’s mass disappears every second?$

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