6. [4 pts] The luminosity of the Sun has been nearly constant over its lifetime.
ID: 1785595 • Letter: 6
Question
6. [4 pts] The luminosity of the Sun has been nearly constant over its lifetime. The solar luminosity is about L = 3.8 × 1026 J/s, and there is evidence that this has remained so for the majority of the Sun’s life so far, about = 4.5 × 109 years. How much mass does the Sun lose by creating energy at its core each second? How much mass has the Sun lost so far in this way? The mass of the Sun is about M = 2 × 1030 kg. What fraction of its present mass has the Sun lost by burning hydrogen? Hydrogen bombs use this same process of hydrogen burning to create energy. A 5-megaton hydrogen bomb releases 3 × 1014 J of energy. A hydrogen bomb is powerful, but not so powerful that it ejects pieces of the Earth into space. Nevertheless, the Earth does lose mass each time we build and detonate a Hydrogen bomb. How much mass does the Earth lose each time a 5-megaton Hydrogen bomb is detonated? Note that 5-megaton doesn’t give the weight of any property of the bomb, it is the equivalent weight of the powerful conventional explosive TNT (trinitrotoluene) that would be needed to duplicate the explosion, in this case 5 million tons.
Explanation / Answer
L = 3.8 x 10^26 J/s
energy provided = (3.8 x 10^26)(4.5 x 10^9 x 365 x 24 x 3600) = 5.393 x 10^43 J
E = m c^2
5.393 x 10^43 = m (3 x 10^8)^2
m = 6 x 10^26 kg .....Ans(mass lost)
fraction = (6 x 10^26) /(2 x 10^30) = 3 x 10^-4 .....Ans
E = ( 5 x 10^9 kg) (3 x 10^14) = 1.5 x 10^24 J
1.5 x 10^24 = m (3 x 10^8)^2
m = 16.7 x 10^6 kg ........Ans
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