A certain star has a mass of 3.2*10^30 kg and radiates energy at the rate of 7.4*10^26 Watts (a) At what rate does the star transfer its mass to other forms of energy? (b) What fraction of its original mass has the star lost in this way since it began to burn hydrogen, 5.2*10^9 years ago?At ? rate a star transfer its energy and What mass frac has star lost in the way?This is an E=mc^2 question.
c^2 is approximately 9 x 10^16 m^2 s^-2.
1 W = 1 J/s. 1 J = 1 kg m^2 s^-2.
Thus 7.4 x 10^26 W is the conversion of about 8.2 x 10^9 kg of matter into energy every second.
5.2 x 10^9 years is 5.2 x 10^9 x 365.24219 x 24 x 3600 seconds = 1.64 x 10^17 seconds.
Consuming matter at 8.2 x 10^9 kg/s over that time leads to the total consumption of 1.35 x 10^27 kg of matter. Which is 0.0004 times the total mass of the star or 0.04%.
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