Question

The sun radiates energy at the rate 3.8*10^26W. 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*10^30kg. Part A) How much mass does the sun lose each year?(delta M)

Part B) What percentage is this of the sun's total mass?

(deltaM/M) %

Part C) Estimate the lifetime of the sun. (t)

Answer 1

Answer:

$1.33243\times 10^{17}\ kg$

$6.69899\times 10^{-12}\%$

$1.49276\times 10^{13}\ years$

Explanation:

P = Power of the Sun = $3.8\times 10^{26}\ W$

c = Speed of light = $3\times 10^8\ m/s$

Annual energy per year is given by

$E=Pt\\\Rightarrow E=3.8\times 10^{26}\times 365.25\times 24\times 3600\\\Rightarrow E=1.19919\times 10^{34}\ J$

From the mass equivalence relation we have

$E=mc^2\\\Rightarrow m=\dfrac{E}{c^2}\\\Rightarrow m=\dfrac{3.8\times 10^{26}\times 365.25\times 24\times 3600}{(3\times 10^8)^2}\\\Rightarrow m=1.33243\times 10^{17}\ kg$

Mass lost in a year is $1.33243\times 10^{17}\ kg$

Percentage mass is given by

$\dfrac{\Delta M}{M}\times 100=\dfrac{1.33243\times 10^{17}}{1.989\times 10^{30}}\times 100\\\Rightarrow \dfrac{\Delta M}{M}\times 100=6.69899\times 10^{-12}\%$

The percentage is $6.69899\times 10^{-12}\%$

Number of years would be the total mass of the sun divided by the mass lost in 1 year

$n=\dfrac{1.989\times 10^{30}}{1.33243\times 10^{17}}\\\Rightarrow n=1.49276\times 10^{13}\ years$

The number of years would be $1.49276\times 10^{13}\ years$