Its very urgent help!

[sizzlingkavya]

Question - The Sun generates its energy via nuclear fusion reactions that convert mass into energy, but the efficiency of this process is only about 0.7% (? = 0.007). Thus, when the Sun fuses 4 nuclei of hydrogen into 1 helium nucleus, about 0.7% of the hydrogen’s rest mass is converted into energy, via E = mc 2, where m is the actual amount of mass that is converted into energy. Moreover, the Sun will convert only about 10% (= 0.10) of its available rest mass into energy before something bad happens … it starts to swell up into a red giant, engulfing the Earth and completely scouring its surface! The luminosity of the Sun is 3.9 x 10^26 Joules / s and its total mass is 1.99 x 10^30 kg. Use these values along with the other information given in this problem and calculate how long we have left before the Earth is devoured by the expanding Sun! (Give your answer in years).

Solution - Mass of the Sun = 1.99 x 10^30kg
dividing by 10 we get
1.99 x 10^29kg
Now E = mc^2
= 1.99 x 10^29 x 3 x 10^8
= 5.97 x 10^37 Joules
now output energy over the earth's life expectancy = 5.97 x 10^37 x 0.007
= 4.179 x 10^35
now sun's luminosity = 3.9 x 10^26J/s

now i got sucked, how can i solve this please its really very urgent help me, I don't have much time.

 

[Deleted member 4993]

Question - The Sun generates its energy via nuclear fusion reactions that convert mass into energy, but the efficiency of this process is only about 0.7% (? = 0.007). Thus, when the Sun fuses 4 nuclei of hydrogen into 1 helium nucleus, about 0.7% of the hydrogen’s rest mass is converted into energy, via E = mc 2, where m is the actual amount of mass that is converted into energy. Moreover, the Sun will convert only about 10% (= 0.10) of its available rest mass into energy before something bad happens … it starts to swell up into a red giant, engulfing the Earth and completely scouring its surface! The luminosity of the Sun is 3.9 x 10^26 Joules / s and its total mass is 1.99 x 10^30 kg. Use these values along with the other information given in this problem and calculate how long we have left before the Earth is devoured by the expanding Sun! (Give your answer in years).

Solution - Mass of the Sun = 1.99 x 10^30kg
dividing by 10 we get
1.99 x 10^29kg
Now E = mc^2
= 1.99 x 10^29 x 3 x 10^8 <<< It should be squared
= 5.97 x 10^37 Joules
now output energy over the earth's (?)life expectancy = 5.97 x 10^37 x 0.007
= 4.179 x 10^35 <<< What's the unit here? That will give yo a hint about what to do.
now sun's luminosity = 3.9 x 10^26J/s

You know total available energy for illumination.

You know the rate at which it is being spent?

How long would it take to spend the whole thing?



now i got sucked, how can i solve this please its really very urgent help me, I don't have much time.

What class are you taking? You are posting different types of problems.