The sun radiates energy at the rate 3.8×1026 W.The source of this energy is fusi

Question

The sun radiates energy at the rate 3.8×1026 W.The source of this energy is fusion, a nuclear reaction in which mass is transformed into energy. The mass of the sun is 2.0×1030 kg.

Part A

How much mass does the sun lose each year?

Express your answer with the appropriate units.

13.3•106kg

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Part B

What percent is this of the sun's total mass?

6.7×1012

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Part C

Fusion takes place in the core of a star, where the temperature and pressure are highest. A star like the sun can sustain fusion until it has transformed about 0.10% of its total mass into energy, then fusion ceases and the star slowly dies. Estimate the sun's lifetime, giving your answer in billions of years.

6.7•1014

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The sun radiates energy at the rate 3.8×1026 W.The source of this energy is fusion, a nuclear reaction in which mass is transformed into energy. The mass of the sun is 2.0×1030 kg.

Part A

How much mass does the sun lose each year?

Express your answer with the appropriate units.

m =

13.3•106kg

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Incorrect; Try Again; 5 attempts remaining

Part B

What percent is this of the sun's total mass?

mM =

6.7×1012

  %  

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Correct

Part C

Fusion takes place in the core of a star, where the temperature and pressure are highest. A star like the sun can sustain fusion until it has transformed about 0.10% of its total mass into energy, then fusion ceases and the star slowly dies. Estimate the sun's lifetime, giving your answer in billions of years.

t =

6.7•1014

  billionyears  

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Incorrect; Try Again; 6 attempts remaining

Explanation / Answer

Power = Eenrgy/time

Energy E = P * t

annual energy E = 3.8 *10^26* 365 days * 24 hrs * 60 min * 60 sec

E = 1.19 *10^34 J

from E = mc^2

m = E/c^2

m = 1.19 *10^34/(3*10^8 *3*10^8)

m = 1.32*10^17 Kg

p---------------------------------------

ratio of masses = M/Ms

= 1.33 *10^17/1.99*10^30

% of ration of masses = 1.32 *10^17/1.99*10^30 *100

% = 6.7 *10^-12 %

------------------------------------
0.1% of mass of sun    = 1.99* 10^30* 0.1/100

mass of sun (new) = 1.99*10^27 kg

total energy E = 1.99 *10^27 * 3*10^8 *3*10^8 = 1.791*10^44 J

Power P = 3.8 *10^26 W

time t = E/P = 1.791*10^44/(3.8 *10^26)

t = 4.71 *10^17 secs   = 1.49 *10^10 years

1 billiion = 10^9 years

t = 15 billion years

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