Main_Sequence - Main Sequence Stars Thermal and...

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Unformatted text preview: Main Sequence Stars Thermal and Gravitational Energy Two large stores of energy in a star are its internal heat (thermal energy) and its gravitational energy. The heat stored in a gas is simply the energy of motion (kinetic energy) of the particles that compose it. If the speeds of these particles decrease, the loss in kinetic energy is radiated away as heat and light. Conservation of Energy The source of heat energy is the chemical burning of objects. Even if the immense mass of the Sun consisted of burnable material, it could not produce energy at its present rate for more than a few thousand years. Geologists have found fossils in rocks that are 3.5 billion years old. Therefore, the Sun must have been heating the Earth nearly that long in order for life to have been maintained. In the 19th century, scientists used the Law of Conservation of Energy to look for a source of energy for the Sun. The law of conservation of energy simply says that energy cannot be created or destroyed, but can be transformed. The reverse is also true. Mechanical motion can be transformed into heat. Gravitational Energy The outer layer of the Sun is a gas, and the temperature is a measure of the atoms’ speeds. If this layer were to fall inward, the atoms would acquire an additional velocity (potential energy is converted to kinetic energy). The star would contract and the atoms would move closer together, increasing the number of collisions, and the temperature would increase. A contraction rate of 40 m/yr would be enough. The amount of energy that has been released since the pre-solar cloud began to contract is on the order of 1042 joules. This is the amount that the Sun could have converted to thermal energy. Since the present luminosity is 3.83 x 1026 watts (J/s) or about 1034 J/yr, this mechanism could have kept the Sun going for 100 million years, but this is much less than the age of the Solar System. Mass, Energy, and Special Relativity Einstein’s Special Theory of Relativity says that mass and energy are equivalent: E = m c2 Mass can be converted to energy, and energy can be converted to mass. The conversion of even a small amount of mass can release great amounts of energy. For the Sun, it takes about 4 million tons of matter converted to energy every second. The Sun has enough mass to continue for about 10 billion years. Interior of the Sun The Gas Pressure can become greater either by increased density or increased speed (temperature). Boyle’s Law states that the pressure of a gas at constant temperature is proportional to its density. Charles’ Law states that the pressure (at constant volume) is proportional to the temperature of the gas. These two ideas combine to give us the Perfect Gas Law: P=nkT where P is the pressure, n is the number of molecules per unit volume, T is the temperature, and k is equal to 1.38 x 10-23 joules/K. Stability Most stars are neither expanding nor contracting. At each point within the star the temperature, pressure, density, etc., are constant values. The mutual gravitational attraction produces tremendous forces that tend to collapse the Sun toward its center. The gravity is counter-balanced by pressure. To exert enough pressure to prevent the collapse due to gravity, the gases at the center of the Sun must be at a temperature of 15 million K. At this temperature protons can fuse into helium nuclei. Gravity Pressure Hydrostatic Equilibrium If the internal pressure were not great enough to balance the weight of its outer parts, the star would collapse somewhat, contracting and building up the pressure inside. If the pressure were greater than the weight of the overlying layers, the star would expand, thus decreasing the internal pressure. Expansion would stop, and equilibrium would be reached, when the pressure at every internal point again equaled the weight of the stellar layers above that point. This condition is called Hydrostatic Equilibrium. Thermal Equilibrium The highest temperature occurs in the center of the star and temperatures drop to successively lower values toward the surface. The outward flow of energy tends to cool an object, were that energy not replaced. So there must be a source of energy within the star. Energy must be supplied to each layer in the star at just the right rate to balance the loss of heat in that layer as it passes energy outward toward the surface. Moreover, the rate at which energy is supplied to the star as a whole must exactly balance the rate at which the whole star loses energy by radiating it into space. The rate of energy production is equal to the luminosity. We call this balance of heat gain and heat loss for the star as a whole and at each point within it the condition of Thermal Equilibrium. PRS Question 1. The phrase “Hydrostatic Equilibrium” refers to a. The balance of gas pressure outward and magnetic forces inward. b. The creation of one He nucleus by the “destruction” of 4 H nuclei. c. The balance of gas pressure inward and heat outward. d. The balance of gravity inward and gas pressure outward. e. The balance of heat gained versus heat lost. Nuclear Fusion Nuclear Physics Key Words: nucleons (protons, neutrons), element, isotope Number of nucleons = A = Z + N where Z is the number of protons N is the number of neutrons New Mass Unit 1 u = 1/12 C12 1 u = 1.660540 x 10-24 g : 931.5 MeV Particle Masses Particle Proton Neutron Electron g 1.672623 x 10-24 1.674929 x 10-24 9.109390 x 10-28 u 1.00727 1.00866 0.00055 MeV 938.27 939.56 0.51 Binding Energy Binding Energy is the energy released due to an accompanying loss in mass when nucleons are combined into atomic nuclei (i.e., fusion). Binding Energy For Example: 4H He 4 mH = 4 x 1.007825 = 4.031280 u 1 mHe = 4.002603 u m = 0.028677 u : 26.71 MeV m / 4 mH = 0.028677 / 4.031280 = 0.0071 = 0.71% Thermonuclear Reactions Conservation of Mass and Energy Conservation of Electric Charge Conservation of Number of Nucleons Conservation of Number of Leptons (electrons & neutrinos) [matter – antimatter] Antimatter e – + e+ 2 Weak Force p+ + e– no + Thermonuclear Reactions Symbols A ZX X: element Z: number of protons (charge) A: mass number = total number of protons and neutrons Proton-Proton I 1 1 H H 1 1 2 1 H e Proton-Proton I 1 1 H H 1 1 2 1 H e Proton-Proton I 1 1 H H 1 1 2 1 H e Proton-Proton I H e 1 1 H H 2 1 2 1 H H 3 2 1 1 1 1 He Proton-Proton I H e 1 1 H H 2 1 2 1 H H 3 2 He 3 2 He He 4 2 He 2 H 1 1 1 1 3 2 69% 1 1 Diagram of PPI PRS Question 2. Apart from the He nuclei that are produced by the PP chain, what are the other by-products? a. rays and neutrinos b. muons, neutrinos, and negative electrons c. positive electrons, rays, and neutrinos d. rays, negative electrons, and neutrinos e. only neutrinos Example Early Proposal for a Hydrogen Bomb: 5 2H 3He + 4He + 1H + 2n 2H 1H n 2.014102 u 1.007825 u 1.008665 u 3He 4He 3.016029 u 4.002603 u There are 5 electrons are on both sides of the reaction, so it is balanced. Example Early Proposal for a Hydrogen Bomb: 5 2H 3He + 4He + 1H + 2n 5 (2.014102) = 10.070510 u 3.016029 + 4.002603 + 1.007825 + (2) 1.008665 = 10.043787 u -------------------Mass Defect = 0.026723 u Q = (0.026723 u) (931.5 MeV/c2) = 24.9 MeV/c2 Nuclear Fusion CNO Cycle 12 6 C 1H 1 13 7 N 13 7 13 6 N C e N 13 6 C 1H 1 14 7 14 7 N 1H 1 15 8 15 8 15 7 O N 1H 1 15 7 O N e 12 6 C 4 2 He Energy Rates Diagram Solar Neutrinos About 3% of the total energy generated by the Sun is carried away by neutrinos. Neutrinos rarely interact with matter, and they travel at the speed of light. If we could devise a way to detect some of the 300 billion solar neutrinos that pass through each square meter of the Earth’s surface every second, then we could obtain information directly about the center of the Sun. 1 1 H H 1 1 2 1 H e Solar Neutrinos But they are hard to detect. On very, very rare occasions, however, a neutrino of the highest energy of those emitted by the Sun will react with the isotope chlorine-37 to produce argon-37 and an electron. The Davis Experiment had a tank of 400,000 liters of cleaning fluid 1.5 km beneath the surface of the Earth in a gold mine. Calculations show that solar neutrinos should produce about one atom of argon-37 daily in this tank. But only about one-third are measured as are predicted. Theory versus Observations The interior is cooler now than when the luminosity was generated a million years ago. There are other types of subatomic particles (WIMPS − weakly interacting massive particles) which are carrying away heat. There are three types of neutrinos, but only one type can interact in the Davis experiment. Possibly the neutrinos can transform themselves during the travel from the Sun to the Earth. PRS Question 3. What happens to the neutrinos produced by the nuclear reactions in the core of the Sun? a. They escape from the Sun into space. b. They combine with protons to form neutrons. c. They collide with electrons, producing energy. d. They collide with protons to form He nuclei. e. They interact with positrons to form deuterium. Interior of the Sun Interior of a High-Mass Star Interior of a Solar-Like Star Interior of a Low-Mass Star Interior Structure A) Core is convective and outer layers are radiative. B) Core is radiative and outer layers are convective. C) Entire star is convective. Radius of A is 4 times that of B; Radius of C is 1/3 that of B. Energy Transport in the Sun Internal Characteristics of the Sun Abundance Changes in the Sun Size Change of the Sun ...
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This note was uploaded on 03/04/2012 for the course PHYS 2022 taught by Professor Jarrio during the Spring '12 term at Central GA Tech.

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