The Sun is powered by nuclear reactions that fuse Hydrogen into Helium. In each

Question

The Sun is powered by nuclear reactions that fuse Hydrogen into Helium. In each reaction, a small amount of mass is converted to energy. Einstein’s famous equation tells us precisely how much energy is liberated for a given mass: E=mc^2

a. The Sun’s luminosity is L = 3.84×10^26 watts. Use Einstein’s equation to determine the rate at which the Sun is losing mass (in kg/s) due to the nuclear reactions that power it. *The speed of light is c = 3×10^8 m/s and 1 watt = (kg m^2)/ (s^3)

b. Determine the total mass lost by the Sun over its entire lifetime of 10^10 years.

Explanation / Answer

The difference in the masses of the Helium nucleus and the 4 protons is 4.6 x10-29kg.

(4 x 1.6725 x 10-27kg) - 6.644 x 10-27kg = 4.6 x10-29kg

E = (4.6 x10-29kg)x( 9.0x1016 m2/s2) = 4.14x10-12 Joules

The number of He nuclei produced each second corresponds to the number of fusion reactions occuring (as each reaction produces one He nucleus.

(3.84x1026 J/s)/(4.14x10-12 J/reaction) = 9.27x1037 reactions (Helium nuclei)/s.

b]

E= mc2

m= E/c2=(3.84 x 1026J)/(9.0 x 1016m2/s2) = 4.27x109kg

(Mass converted/reaction)x( of reactions/sec) = Mass converted/sec

t=1010 yrs=31,536,000 * 1010 seconds

Mass converted/sec= (4.6x10-29kg)x(9.27 x1037 reactions/31,536,000 * 1010sec)

= 4.35x109/31,536,000 * 1010seckg/s= 1.38*10-8 kg/sec

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