PLEASE ANSWER ALL PARTS AND I WILL RATE THE BEST ANSWER. THANK YOU. A Surprising
ID: 1497435 • Letter: P
Question
PLEASE ANSWER ALL PARTS AND I WILL RATE THE BEST ANSWER. THANK YOU.
A Surprising consequence of Special Relativity is the equivalence of mass and energy that is described by Einstein’s well-known equation E=mc^2 Use the equivalence of mass and energy to answer the following questions.
A. The Sun’s luminosity is 3.8 x 1026 joules/second. How many tons of matter destroyed each second to produce this energy? You may assume that 1 ton = 907 kg.
B. We measure nuclear explosives in terms of kilotons of TNT (the bomb that destroyed Hiroshima in WWII was a 20 kiloton weapon). 1 kiloton = 4.19 x 1012 Joules. How many Hiroshima-type bombs would you have to explode every second to equal the Sun’s energy output?
C. If a star converted every bit of its mass into energy the conversion efficiency would be 100%. However, the Sun converts hydrogen into helium with an efficiency of only 0.7%. The Sun has a mass of 2 x 1030 kg. How long will the Sun live if it converts all of its hydrogen into helium?
Explanation / Answer
A) m = E / c2 = (3.8 x1026) / (3x108) = 1266 x 1015 kg = 1.396 x 1015 Tons
B) (3.8 x1026) / (4.19 x 1012) = 90.69 x 1012 kilotons of TNT = 4.535 x 1012 Hiroshima-Bombs
C) E= (2x1030) (3x108)2 =18 x 1046 J
But 0.7 % efficiency,E= 7x 10-3 x18 x 1046 J = 126 x 1043 J
For life of sun, 126 x 1043 /3.8 x1026 = 33.15789 x 1017 seconds = 1.05143 x1011 Years
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