Astronomy
1st Edition
ISBN: 9781938168284
Author: Andrew Fraknoi; David Morrison; Sidney C. Wolff
Publisher: OpenStax
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Textbook Question
Chapter 16, Problem 37E
Every 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
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Problem 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?
The energy of a moving object is given by the equation of E-mv². What is the
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Can you solve the problem, according to the information provided?
Chapter 16 Solutions
Astronomy
Ch. 16 - How do we know the age of the Sun?Ch. 16 - Explain how we know that the Sun’s energy is not...Ch. 16 - What is the ultimate source of energy that makes...Ch. 16 - What are the formulas for the three steps in the...Ch. 16 - How is a neutrino different from a neutron? List...Ch. 16 - Describe in your own words what is meant by the...Ch. 16 - Two astronomy students travel to South Dakota. One...Ch. 16 - What do measurements of the number of neutrinos...Ch. 16 - Do neutrinos have mass? Describe how the answer to...Ch. 16 - Neutrinos produced in the core of the Sun carry...
Ch. 16 - What conditions are required before proton-proton...Ch. 16 - Describe the two main ways that energy travels...Ch. 16 - Someone suggests that astronomers build a special...Ch. 16 - Earth contains radioactive elements whose decay...Ch. 16 - The Sun is much larger and more massive than...Ch. 16 - A friend who has not had the benefit of an...Ch. 16 - Which of the following transformations is (are)...Ch. 16 - Why is a higher temperature required to fuse...Ch. 16 - Earth’s atmosphere is in hydrostatic equilibrium....Ch. 16 - Explain what it means when we say that Earth’s...Ch. 16 - What mechanism transfers heat away from the...Ch. 16 - Suppose you are standing a few feet away from a...Ch. 16 - Give some everyday examples of the transport of...Ch. 16 - Suppose the proton-proton cycle in the Sun were to...Ch. 16 - Do you think that nuclear fusion takes place in...Ch. 16 - Why is fission not an important energy source in...Ch. 16 - Why do you suppose so great a fraction of the...Ch. 16 - Explain how mathematical computer models allow us...Ch. 16 - Estimate the amount of mass that is converted to...Ch. 16 - How much energy is released when a proton combines...Ch. 16 - The Sun converts 4109 kg of mass to energy every...Ch. 16 - Assume that the mass of the Sun is 75% hydrogen...Ch. 16 - In fact, the conversion of mass to energy in the...Ch. 16 - Now suppose that all of the hydrogen atoms in the...Ch. 16 - Models of the Sun indicate that only about 10% of...Ch. 16 - Show that the statement in the text is correct:...Ch. 16 - Every second, the Sun converts 4 million tons of...Ch. 16 - Raymond Davis Jr.’s neutrino detector contained...
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Need a deep-dive on the concept behind this application? Look no further. Learn more about this topic, physics and related others by exploring similar questions and additional content below.Similar questions
- Which 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_forwardRaising a number in scientific notation to a power is easy: (5 x 105)² = (5)² x (105)² = 5 x 5 x 105 x 105 = 25 x 10(5 × 2) = 25 x 1010 = 2.5 x 101¹1 Keeping this in mind, what is the volume of the sun in km³? The radius of the sun is about 7 x 105 km, and the volume of a sphere is 4/3 x Pi x R³. (Use 3.14 for Pi, and enter your answer with two decimal places). km³ 3 What is the average density of the Sun? Density = mass / volume. The mass of the sun is 2.0x10³0 kg. kg/km³arrow_forwardAssume that Hydrogen comprises 78% of the Sun’s mass. How much mass is this?arrow_forward
- 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?arrow_forwardNow 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_forwardIn fact, the conversion of mass to energy in the Sun is not 100% efficient. As we have seen in the text, the conversion of four hydrogen atoms to one helium atom results in the conversion of about 0.02862 times the mass of a proton to energy. How much energy in joules does one such reaction produce? (See Appendix E for the mass of the hydrogen atom, which, for all practical purposes, is the mass of a proton.)arrow_forward
- The meter was redefined as a reference to Earth, then to krypton, and finally to the speed of light. Why do you think the reference point for a meter continued to change?arrow_forwardThe 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_forwardIn 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 0.00arrow_forward
- Use the equation E = mc^2 where E is energy in Joules (J), m is mass in kilograms (kg) and c is the speed of light 3 x 10^8 m/s to answer the following: a) One ton of TNT releases 4.18 gigajoules of energy. The metric prefix giga means billion. a) How much mass would be required to release an equivalent amount of energy? b) How much energy (J) is equivalent to 1 kilogram of mass?arrow_forwardCarbon-14 (14C) is a radioactive isotope of carbon with a half-life of 5730 years—meaning that half of the 14C in a sample decays into 14N during that time. Suppose a scientist analyzes a sample of ancient plant material from a bog and finds that it contains 1/8th as much 14C as when it formed. Roughly how old is the sample? _____ yearsarrow_forwardFor a satellite launched to an altitude of 800 km, is there any significant difference to the lifetime depending on the phase of the solar cycle at launch? Explain your answer.arrow_forward
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