Chapter 36: Q. 69 (page 1062)

The sun radiates energy at the rate $3.8 \times 10^{26} W$ . The source of this energy is fusion, a nuclear reaction in which mass is transformed into energy. The mass of the sun is $2.0 \times 10^{30} kg$ .
a. How much mass does the sun lose each year?
b. What percent is this of the sun’s total mass?
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.

Short Answer

Expert verified

a. mass of the sun used in one year is $1.33 \times 10^{17} kg .$

b. Percentage is $6.65 \times 10^{- 12} % .$

c. Sun lifetime is $1.5 \times 10^{13} years .$

Step by step solution

Part (a) Step 1: Given information

We have given,

power = $3.8 \times 10^{26} W$

Mass of sun = $2.0 \times 10^{30} kg$

We have to find the mass used in fusion in one year.

Simplify

The Energy obtain by sun in one year time,

$E = Pt E = 3.8 \times 10^{26} W \times 31536000 s E = 1.2 \times 10^{34} J$

Then, mass will be,

$E = {mc}^{2} 1.2 \times 10^{34} J = mc m = 1.33 \times 10^{17} kg$

Part (b) Step 1: Given information

We have given,

Mass of the sun = $2.0 \times 10^{30} kg$

We have to find the percentage of mass used.

Simplify

$% = \frac{m_{used}}{m_{total}} \times 100 % = \frac{1.33 \times 10^{17} kg}{2 \times 10^{30} kg} \times 100 % = 6.65 \times 10^{- 12}$

Part (c) Step 1: Given information

We have to find the life time of the sun.

Simplify

$T = \frac{total mass}{rate of fusion} T = \frac{2 \times 10^{30}}{1.33 \times 10^{17}} T = 1.5 \times 10^{13} years .$

Unlock Step-by-Step Solutions & Ace Your Exams!

Full Textbook Solutions
Get detailed explanations and key concepts
Unlimited Al creation
Al flashcards, explanations, exams and more...
Ads-free access
To over 500 millions flashcards
Money-back guarantee
We refund you if you fail your exam.

Start your free trial

Over 30 million students worldwide already upgrade their learning with Vaia!

Recommended explanations on Physics Textbooks

View all explanations

What do you think about this solution?

We value your feedback to improve our textbook solutions.

Short Answer

Step by step solution

Part (a) Step 1: Given information

Simplify

Part (b) Step 1: Given information

Simplify

Part (c) Step 1: Given information

Simplify

One App. One Place for Learning.

Most popular questions from this chapter

Recommended explanations on Physics Textbooks

Electrostatics

Further Mechanics and Thermal Physics

Rotational Dynamics

Electromagnetism

Translational Dynamics

Nuclear Physics

Study anywhere. Anytime. Across all devices.