21st Century Astronomy
6th Edition
ISBN: 9780393428063
Author: Kay
Publisher: NORTON
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Chapter 14, Problem 36QP
To determine
The mass to be converted into energy.
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Students have asked these similar questions
Assume that Hydrogen comprises 78% of the Sun’s mass. How much mass is this?
In the model shown in the table below, what fraction of the Sun's mass is hotter than 5,000,000 K?
R/R SunT (106 K) Density (g/cm³)
1.00
0.90
0.80
0.70
0.60
0.50
0.40
0.30
0.20
0.10
0.00
0.006
0.60
1.2
2.3
3.1
4.9
5.1
6.9
9.3
13.1
15.7
0.00
0.009
0.035
0.12
0.40
1.3
4.1
13
36
89
150
M/M Sun L/L Sun
1.00
0.999
0.996
0.990
0.97
0.92
0.82
0.63
0.34
0.073
0.000
1.00
1.00
1.00
1.00
1.00
1.00
1.00
0.99
0.91
0.40
0.00
The total energy output from the Sun of around 3.8 x 1026 joules per second, what is the mass of elements consumed in order to produce this amount of energy?
Chapter 14 Solutions
21st Century Astronomy
Ch. 14.1 - Prob. 14.1ACYUCh. 14.1 - Prob. 14.1BCYUCh. 14.2 - Prob. 14.2CYUCh. 14.3 - Prob. 14.3CYUCh. 14.4 - Prob. 14.4CYUCh. 14 - Prob. 1QPCh. 14 - Prob. 2QPCh. 14 - Prob. 3QPCh. 14 - Prob. 4QPCh. 14 - Prob. 5QP
Ch. 14 - Prob. 6QPCh. 14 - Prob. 7QPCh. 14 - Prob. 8QPCh. 14 - Prob. 9QPCh. 14 - Prob. 10QPCh. 14 - Prob. 11QPCh. 14 - Prob. 12QPCh. 14 - Prob. 13QPCh. 14 - Prob. 14QPCh. 14 - Prob. 15QPCh. 14 - Prob. 16QPCh. 14 - Prob. 17QPCh. 14 - Prob. 18QPCh. 14 - Prob. 19QPCh. 14 - Prob. 20QPCh. 14 - Prob. 21QPCh. 14 - Prob. 22QPCh. 14 - Prob. 23QPCh. 14 - Prob. 24QPCh. 14 - Prob. 25QPCh. 14 - Prob. 26QPCh. 14 - Prob. 27QPCh. 14 - Prob. 28QPCh. 14 - Prob. 29QPCh. 14 - Prob. 30QPCh. 14 - Prob. 31QPCh. 14 - Prob. 34QPCh. 14 - Prob. 35QPCh. 14 - Prob. 36QPCh. 14 - Prob. 37QPCh. 14 - Prob. 38QPCh. 14 - Prob. 39QPCh. 14 - Prob. 40QPCh. 14 - Prob. 41QPCh. 14 - Prob. 42QPCh. 14 - Prob. 43QPCh. 14 - Prob. 44QPCh. 14 - Prob. 45QP
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- Now suppose that all of the hydrogen atoms in the Sun were converted into helium. How much total energy would be produced? (To calculate the answer, you will have to estimate how many hydrogen atoms are in the Sun. This will give you good practice with scientific notation, since the numbers involved are very large! See Appendix C for a review of scientific notation.)arrow_forwardEvery second, the Sun converts 4 million tons of matter to energy. How long will it take the Sun to reduce its mass by 1% (the mass of the Sun is 21030 kg)? Compare your answer with the lifetime of the Sun so far.arrow_forwardProblem 1. Mass-Energy conversion in the Sun (Palen, et. al. 3rd Edition, Chapter 11, problems 38, 39) The Sun produces energy by converting mass m into energy E according to E = mc2 where c is the speed of light (c = 300,000 km/sec). Show that if the Sun produces 3.85 × 1026 joules (J) of energy per second, it must convert 4.3 billion kg of mass per second into energy. Note that 1 J/s is a watt (W), which may be more familiar to you. How much mass has the Sun lost over its lifetime (4.5 billion years)? The current mass of the Sun is 2 × 1030. What fraction of this mass has been converted into energy during the Sun’s lifetime?arrow_forward
- Let's examine how we know that the Sun cannot power itself by chemical reactions. Using the fact that an average chemical reaction between two atoms releases 1.6×10-19 J of energy, estimate how long the Sun could emit energy at its current luminosity. Compare that estimate to the known age of Earth.arrow_forwardThe Sun is currently about 4.4 billion years old. How much longer does it have before it runs out of Hydrogen? Answer in billions of years.arrow_forward(The answer for 1 is not 0.000095 solar masses/year)arrow_forward
- The sun’s energy comes from nuclear reactions that fuse lighter nuclei into heavier ones, releasing energy in the process. The solar fusion process begins when two protons (the nuclei of hydrogen atoms) merge to produce a deuterium nucleus. Deuterium is the “heavy” isotope of hydrogen, with a nucleus consisting of a proton and a neutron. To become deuterium, one of the protons that fused has to turn into a neutron. Our interest for now lies not with the nuclear physics but with the conditions that allow fusion to occur. Before two protons can fuse, they must come into contact. However, the energy required to bring two protons into contact is considerable because the electric potential energy of the two protons increases rapidly as they approach each other. Fusion occurs in the core of the sun because the ultra-high temperature there gives the protons the kinetic energy they need to come together. a. A proton…arrow_forwardWhat changes would you notice if the sun emitted radiation at an effective temperature of 2000 K instead of 5762 K.arrow_forwardOnly about 11% of the initial Hydrogen in the Sun is in the core where it is hot enough to burn. What was the total mass of the initial H in the core of the Sun? (Mass of the Sun is 1.989 × 10^30 kg)arrow_forward
- Assume that the core of the Sun has one-eighth of the Sun’s mass and is compressed within a sphere whose radius is one-fourth of the solar radius.Assume further that the composition of the core is 35% hydrogen by mass and that essentially all the Sun’s energy is generated there. If the Sun continues to burn hydrogen at the current rate of 6.2 *1011 kg/s, how long will it be before the hydrogen is entirely consumed? The Sun’s mass is 2.0 * 1030 kg.arrow_forwardWhich of the following is least reasonable regarding energy production in the Sun? Group of answer choices Although the Sun is losing some energy, it is getting bigger and gaining some mass because some of the radiated energy is being converted to mass. The core of the Sun is converting hydrogen to helium through nuclear fusion. Some of the energy produced in the Sun through nuclear fusion can be harnessed on Earth with photovoltaic (e.g., solar panels) technology. The mass m lost in a nuclear fusion reaction can be accounted for by a gain of energy E according to the famous equation E=mc2.arrow_forwardA solar flare can release 1025 J. How many megatons of TNT would be equivalent?arrow_forward
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