UNDERSTANDING THE UNIVERSE(LL)-W/CODE
3rd Edition
ISBN: 9780393869903
Author: PALEN
Publisher: NORTON
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Chapter 11, Problem 40QAP
To determine
The lifetime of the Sun.
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Assuming that (1) the solar luminosity has been constant since the Sun formed, and (2) the Sun was initially of uniform composition throughout, as described by Table 9.2, estimate how long it would take the Sun to convert all of its original hydrogen into helium. [Hint: Calculate the mass of hydrogen in the sun and then divide it by the rate of hydrogen fusion (PPT slide 47.)]
The Sun’s luminosity (or power) is 4 x 1026 Watts (=J/s). How many kilograms of hydrogen must be fused every second to maintain this luminosity? (hint: work backwards from the energy per second to the mass released to the amount of hydrogen required, using the results from the previous question.)
The Sun’s mass is ~2x1030 kg. If 10% of this is Hydrogen available in the core, how long will the Sun be able to continue fusing hydrogen at this rate? This is considered the Sun's "lifetime". If the Sun is 4.6 billion years old (and assuming it's power output is constant), how many years does it have left?
Assume that Hydrogen comprises 79% of the Sun's mass. How much mass is this? 1.57e+30 kg
Only 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 inital H in the core of the Sun?
Hint: Use the answer above and the percent in the core to determine the total mass.
Using the results from above, how much total energy is available to the Sun via nuclear fusion over its lifetime? (HINT: only 0.71% of the total mass of the available H in the core is converted into energy)
Hint: E = m c^2
Chapter 11 Solutions
UNDERSTANDING THE UNIVERSE(LL)-W/CODE
Ch. 11.1 - Prob. 11.1CYUCh. 11.2 - Prob. 11.2CYUCh. 11.3 - Prob. 11.3CYUCh. 11.4 - Prob. 11.4CYUCh. 11 - Prob. 1QAPCh. 11 - Prob. 2QAPCh. 11 - Prob. 3QAPCh. 11 - Prob. 4QAPCh. 11 - Prob. 5QAPCh. 11 - Prob. 6QAP
Ch. 11 - Prob. 7QAPCh. 11 - Prob. 8QAPCh. 11 - Prob. 9QAPCh. 11 - Prob. 10QAPCh. 11 - Prob. 11QAPCh. 11 - Prob. 12QAPCh. 11 - Prob. 13QAPCh. 11 - Prob. 14QAPCh. 11 - Prob. 15QAPCh. 11 - Prob. 16QAPCh. 11 - Prob. 17QAPCh. 11 - Prob. 18QAPCh. 11 - Prob. 19QAPCh. 11 - Prob. 20QAPCh. 11 - Prob. 21QAPCh. 11 - Prob. 22QAPCh. 11 - Prob. 23QAPCh. 11 - Prob. 24QAPCh. 11 - Prob. 25QAPCh. 11 - Prob. 26QAPCh. 11 - Prob. 27QAPCh. 11 - Prob. 28QAPCh. 11 - Prob. 29QAPCh. 11 - Prob. 30QAPCh. 11 - Prob. 31QAPCh. 11 - Prob. 32QAPCh. 11 - Prob. 33QAPCh. 11 - Prob. 34QAPCh. 11 - Prob. 35QAPCh. 11 - Prob. 36QAPCh. 11 - Prob. 37QAPCh. 11 - Prob. 38QAPCh. 11 - Prob. 39QAPCh. 11 - Prob. 40QAPCh. 11 - Prob. 41QAPCh. 11 - Prob. 42QAPCh. 11 - Prob. 43QAPCh. 11 - Prob. 44QAPCh. 11 - Prob. 45QAP
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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
- Can you solve the problem, according to the information provided?arrow_forwardShow that the statement that 92% of the Sun’s atoms are hydrogen is consistent with the statement that 73% of the Sun’s mass is made up of hydrogen, as found in Table 15.2. (Hint: Make the simplifying assumption, which is nearly correct, that the Sun is made up entirely of hydrogen and helium.)arrow_forwardWhy do you suppose so great a fraction of the Sun’s energy comes from its central regions? Within what fraction of the Sun’s radius does practically all of the Sun’s luminosity originate (see Figure 16.16)? Within what radius of the Sun has its original hydrogen been partially used up? Discuss what relationship the answers to these questions bear to one another. Figure 16.16 shows how the temperature, density, rate of energy generation, and composition vary from the center of the Sun to its surface.arrow_forward
- 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_forwardHow do we know the age of the Sun?arrow_forwardFrom the information in Figure 15.21, estimate the speed with which the particles in the CME in parts (c) and (d) are moving away from the Sun. Figure 15.21 Flare and Coronal Mass Ejection. This sequence of four images shows the evolution over time of a giant eruption on the Sun. (a) The event began at the location of a sunspot group, and (b) a flare is seen in far-ultraviolet light. (c) Fourteen hours later, a CME is seen blasting out into space. (d) Three hours later, this CME has expanded to form a giant cloud of particles escaping from the Sun and is beginning the journey out into the solar system. The white circle in (c) and (d) shows the diameter of the solar photosphere. The larger dark area shows where light from the Sun has been blocked out by a specially designed instrument to make it possible to see the faint emission from the corona. (credit a, b, c, d: modification of work by SOHO/EIT, SOHO/LASCO, SOHO/MDI (ESA & NASA))arrow_forward
- Do you think that nuclear fusion takes place in the atmospheres of stars? Why or why not?arrow_forwardSummarize the evidence indicating that over several hundreds of years or more there have been variations in the level of the solar activity.arrow_forwardDo the previous problem again, this time using the information that the Sun is 150,000,000 km away. You will get a very large number of km as your answer. To get a better feeling for how the distances compare, try calculating the time it takes light at a speed of 299,338 km/s to travel from the Sun to Earth and from Alpha Centauri to Earth. For Alpha Centauri, figure out how long the trip will take in years as well as in seconds.arrow_forward
- Models of the Sun indicate that only about 10% of the total hydrogen in the Sun will participate in nuclear reactions, since it is only the hydrogen in the central regions that is at a high enough temperature. Use the total energy radiated per second by the Sun, 3.81026 watts, alongside the exercises and information given here to estimate the lifetime of the Sun. (Hint: Make sure you keep track of the units: if the luminosity is the energy radiated per second, your answer will also be in seconds. You should convert the answer to something more meaningful, such as years.)arrow_forwardHow much mass would need to be converted to energy in one hour to provide the sun with 1.378x10^30 j? (Remember that 1 j = 1kg m^2 s-^2 give your answer to 2 sig figures you may assume that c=3.0x10^8 ms-^1arrow_forwardThe total luminosity of the Sun is 4e26 Watts.a) What is the mass (in kg) that the Sun loses each second due to the conversion of nuclearbinding energy into radiation?b) The Sun has a total mass of 2e30kg and will live for 1e10 years. What fraction of theSun’s mass will be consumed in its lifetime due to nuclear fusion? Don’t forget that Wattsare measured in seconds.c) One of the interactions that takes place in the Sun’s core is the production of Deuterium.Two protons come together and one converts into a neutron. The mass of each proton is938.27209 MeV/c2. The mass of the deuteron is 1875.61294 MeV. How much energy isreleased during this process?d) During this process, the new nucleus releases two other particles. The initial particles,two protons, each have a quantum spin of +1/2 and an electric charge of +1. Now you havea proton, a neutron, a particle X, and particle Y. If the particle X has no electric charge,what is the electric charge of particle Y? If particle Y has a spin of…arrow_forward
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