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

The Sun loses mass each year due to fusion. To calculate the mass lost, we use Einstein's equation E = mc². We can also determine the percentage of mass lost and estimate the lifetime of the Sun.

Step-by-step explanation:

Part A) To calculate the mass that the Sun loses each year, we can use Einstein's equation E = mc². The power output of the Sun is given as 3.8 × 10²6 W, which is the energy produced per second. We can convert this energy into mass by rearranging the equation: E = mc². Solving for mass, we get m = E/c². Plugging in the values, we have m = (3.8 × 10²6)/(3.0 × 10^8)². Evaluating this expression gives us the mass lost per second. To find the mass lost each year, we need to multiply this value by the number of seconds in a year.

Part B) To find the percentage of the Sun's total mass that is lost each year, we need to divide the mass lost each year by the total mass of the Sun and multiply by 100.

Part C) To estimate the lifetime of the Sun, we need to divide the total mass of the Sun by the mass lost each year. This will give us the number of years it takes for the Sun to lose all its mass.

Answer 2

`1.33243* 10^(17)\ kg`

`6.69899* 10^(-12)\%`

`1.49276* 10^(13)\ years`

Step-by-step explanation:

P = Power of the Sun =
`3.8* 10^(26)\ W`

c = Speed of light =
`3* 10^8\ m/s`

Annual energy per year is given by

`E=Pt\\\Rightarrow E=3.8* 10^(26)* 365.25* 24* 3600\\\Rightarrow E=1.19919* 10^(34)\ J`

From the mass equivalence relation we have

`E=mc^2\\\Rightarrow m=(E)/(c^2)\\\Rightarrow m=(3.8* 10^(26)* 365.25* 24* 3600)/((3* 10^8)^2)\\\Rightarrow m=1.33243* 10^(17)\ kg`

Mass lost in a year is
`1.33243* 10^(17)\ kg`

Percentage mass is given by

`(\Delta M)/(M)* 100=(1.33243* 10^(17))/(1.989* 10^(30))* 100\\\Rightarrow (\Delta M)/(M)* 100=6.69899* 10^(-12)\%`

The percentage is
`6.69899* 10^(-12)\%`

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

`n=(1.989* 10^(30))/(1.33243* 10^(17))\\\Rightarrow n=1.49276* 10^(13)\ years`

The number of years would be
`1.49276* 10^(13)\ years`