The Sun
<Text-field style="Heading 1" layout="Heading 1">Introduction</Text-field> For the Sun, calculate the (A) central pressure, (B) central temperature, (C) pressure scale height, (D) adiabatic sound speed for a monatomic gas, and (E) the adiabatic convection by Mixing-length Theory. Data are from Bahcall, Basu & Pinsonneault (1998), Basu & Antia (1997), Langer (2016), and Mullan (2010). LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYjLUkjbW9HRiQ2LlEhRicvJStleGVjdXRhYmxlR1EmZmFsc2VGJy8lLG1hdGh2YXJpYW50R1Enbm9ybWFsRicvJSZmZW5jZUdGMS8lKnNlcGFyYXRvckdGMS8lKXN0cmV0Y2h5R0YxLyUqc3ltbWV0cmljR0YxLyUobGFyZ2VvcEdGMS8lLm1vdmFibGVsaW1pdHNHRjEvJSdhY2NlbnRHRjEvJSdsc3BhY2VHUSYwLjBlbUYnLyUncnNwYWNlR0ZF Hints The central pressure, when calculated, will be needed in some further calculations. The pressure due to radiation is very small and can be ignored. Care should be taken to use the correct data in the various problems. For example, the mean molecular weight at the core (LUkjbWlHNiMvSSttb2R1bGVuYW1lRzYiSSxUeXBlc2V0dGluZ0dJKF9zeXNsaWJHRic2JlElJm11O0YnLyUnaXRhbGljR1EmZmFsc2VGJy8lK2V4ZWN1dGFibGVHRi4vJSxtYXRodmFyaWFudEdRJ25vcm1hbEYn - used in problem B) is not the same as the average mean molecular weight (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 in problem E). LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYnLUkjbWlHRiQ2JVEocmVzdGFydEYnLyUnaXRhbGljR1EldHJ1ZUYnLyUsbWF0aHZhcmlhbnRHUSdpdGFsaWNGJy1JI21vR0YkNi1RIjpGJy9GM1Enbm9ybWFsRicvJSZmZW5jZUdRJmZhbHNlRicvJSpzZXBhcmF0b3JHRj0vJSlzdHJldGNoeUdGPS8lKnN5bW1ldHJpY0dGPS8lKGxhcmdlb3BHRj0vJS5tb3ZhYmxlbGltaXRzR0Y9LyUnYWNjZW50R0Y9LyUnbHNwYWNlR1EsMC4yNzc3Nzc4ZW1GJy8lJ3JzcGFjZUdGTC8lJ2ZhbWlseUdRMFRpbWVzfk5ld35Sb21hbkYnLyUrZXhlY3V0YWJsZUdGPUY5 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
<Text-field style="Heading 1" layout="Heading 1">Data</Text-field> Mass of Sun 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 Radius of Sun 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 JSFH JSFH Gravitational Constant 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 = 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 Mean molecular weight at the core 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 Average mean molecular weight 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 LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYjLUkjbW9HRiQ2LlEhRicvJStleGVjdXRhYmxlR1EmZmFsc2VGJy8lLG1hdGh2YXJpYW50R1Enbm9ybWFsRicvJSZmZW5jZUdGMS8lKnNlcGFyYXRvckdGMS8lKXN0cmV0Y2h5R0YxLyUqc3ltbWV0cmljR0YxLyUobGFyZ2VvcEdGMS8lLm1vdmFibGVsaW1pdHNHRjEvJSdhY2NlbnRHRjEvJSdsc3BhY2VHUSYwLjBlbUYnLyUncnNwYWNlR0ZF Mass of the hydrogen atom 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 JSFH Boltzmann's constant LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYpLUkjbWlHRiQ2JVEia0YnLyUnaXRhbGljR1EldHJ1ZUYnLyUsbWF0aHZhcmlhbnRHUSdpdGFsaWNGJy1JI21vR0YkNi1RKiZjb2xvbmVxO0YnL0YzUSdub3JtYWxGJy8lJmZlbmNlR1EmZmFsc2VGJy8lKnNlcGFyYXRvckdGPS8lKXN0cmV0Y2h5R0Y9LyUqc3ltbWV0cmljR0Y9LyUobGFyZ2VvcEdGPS8lLm1vdmFibGVsaW1pdHNHRj0vJSdhY2NlbnRHRj0vJSdsc3BhY2VHUSwwLjI3Nzc3NzhlbUYnLyUncnNwYWNlR0ZMLUYjNigtRiw2JlEpR2V0VmFsdWVGJ0YvLyUwZm9udF9zdHlsZV9uYW1lR1EpMkR+SW5wdXRGJ0YyLUkobWZlbmNlZEdGJDYlLUYjNiUtRiw2JlEpQ29uc3RhbnRGJ0YvRlRGMi1GWDYlLUYjNiYtRjY2LlEiJ0YnRlRGOUY7Rj5GQEZCRkRGRkZIL0ZLUSwwLjExMTExMTFlbUYnL0ZOUSYwLjBlbUYnLUYsNiZGLkYvRlRGMkZdb0Y5RlRGOUY5RlRGOS1GNjYuUScmc2RvdDtGJ0ZURjlGO0Y+RkBGQkZERkZGSC9GS0Zjb0Ziby1GLDYmUShHZXRVbml0RidGL0ZURjJGV0Y5LUY2Ni5RIUYnLyUrZXhlY3V0YWJsZUdGPUY5RjtGPkZARkJGREZGRkhGaW9GYm8vJSdmYW1pbHlHUTBUaW1lc35OZXd+Um9tYW5GJ0ZgcEY5 = 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 Average solar density 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 LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYjLUkjbW9HRiQ2LlEhRicvJStleGVjdXRhYmxlR1EmZmFsc2VGJy8lLG1hdGh2YXJpYW50R1Enbm9ybWFsRicvJSZmZW5jZUdGMS8lKnNlcGFyYXRvckdGMS8lKXN0cmV0Y2h5R0YxLyUqc3ltbWV0cmljR0YxLyUobGFyZ2VvcEdGMS8lLm1vdmFibGVsaW1pdHNHRjEvJSdhY2NlbnRHRjEvJSdsc3BhY2VHUSYwLjBlbUYnLyUncnNwYWNlR0ZF Density at the base of the convection zone 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 LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYjLUkjbW9HRiQ2LlEhRicvJStleGVjdXRhYmxlR1EmZmFsc2VGJy8lLG1hdGh2YXJpYW50R1Enbm9ybWFsRicvJSZmZW5jZUdGMS8lKnNlcGFyYXRvckdGMS8lKXN0cmV0Y2h5R0YxLyUqc3ltbWV0cmljR0YxLyUobGFyZ2VvcEdGMS8lLm1vdmFibGVsaW1pdHNHRjEvJSdhY2NlbnRHRjEvJSdsc3BhY2VHUSYwLjBlbUYnLyUncnNwYWNlR0ZF LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYjLUkjbW9HRiQ2LlEhRicvJStleGVjdXRhYmxlR1EmZmFsc2VGJy8lLG1hdGh2YXJpYW50R1Enbm9ybWFsRicvJSZmZW5jZUdGMS8lKnNlcGFyYXRvckdGMS8lKXN0cmV0Y2h5R0YxLyUqc3ltbWV0cmljR0YxLyUobGFyZ2VvcEdGMS8lLm1vdmFibGVsaW1pdHNHRjEvJSdhY2NlbnRHRjEvJSdsc3BhY2VHUSYwLjBlbUYnLyUncnNwYWNlR0ZF Solar luminence 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 distance from centre to the base of the convection zone 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 JSFH Universal gas constant 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 = 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 JSFH Particle number densityJSFH JSFH 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 = 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 Temperatyre at the base of the convection zone 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JSFHJSFH
<Text-field style="Heading 1" layout="Heading 1">Useful Equations</Text-field> Equation to approximate the central pressure of a star 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LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYjLUkjbW9HRiQ2LlEhRicvJStleGVjdXRhYmxlR1EmZmFsc2VGJy8lLG1hdGh2YXJpYW50R1Enbm9ybWFsRicvJSZmZW5jZUdGMS8lKnNlcGFyYXRvckdGMS8lKXN0cmV0Y2h5R0YxLyUqc3ltbWV0cmljR0YxLyUobGFyZ2VvcEdGMS8lLm1vdmFibGVsaW1pdHNHRjEvJSdhY2NlbnRHRjEvJSdsc3BhY2VHUSYwLjBlbUYnLyUncnNwYWNlR0ZF Adiabatic sound speed LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYoLUkjbW9HRiQ2LlEhRicvJStleGVjdXRhYmxlR1EmZmFsc2VGJy8lLG1hdGh2YXJpYW50R1Enbm9ybWFsRicvJSZmZW5jZUdGMS8lKnNlcGFyYXRvckdGMS8lKXN0cmV0Y2h5R0YxLyUqc3ltbWV0cmljR0YxLyUobGFyZ2VvcEdGMS8lLm1vdmFibGVsaW1pdHNHRjEvJSdhY2NlbnRHRjEvJSdsc3BhY2VHUSYwLjBlbUYnLyUncnNwYWNlR0ZFLUYjNiktSSNtaUdGJDYnUSJ2RicvJSdpdGFsaWNHUSV0cnVlRidGLy8lMGZvbnRfc3R5bGVfbmFtZUdRKTJEfklucHV0RicvRjNRJ2l0YWxpY0YnLUkobWZlbmNlZEdGJDYoLUYjNiYtRks2J1Eic0YnRk5GL0ZRRlRGL0ZRRjJGL0ZRRjIvJSVvcGVuR1EiW0YnLyUmY2xvc2VHUSJdRictRiw2L1EiPUYnRi9GUUYyRjVGN0Y5RjtGPUY/RkEvRkRRLDAuMjc3Nzc3OGVtRicvRkdGYm8tSSVtc3VwR0YkNiUtRlc2Ji1GIzYmLUkmbWZyYWNHRiQ2KC1GIzYpLUkjbW5HRiQ2JlEiNUYnRi9GUUYyLUYsNi9RJyZzZG90O0YnRi9GUUYyRjVGN0Y5RjtGPUY/RkFGQ0ZGLUZLNidRIlBGJ0ZORi9GUUZULUZXNigtRiM2Ji1GSzYnUSNhdkYnRk5GL0ZRRlRGL0ZRRjJGL0ZRRjJGaG5GW29GL0ZRRjItRiM2KC1GYXA2JlEiM0YnRi9GUUYyRmRwLUZLNidRJiZyaG87RicvRk9GMUYvRlFGMkYvRlFGMi8lLmxpbmV0aGlja25lc3NHUSIxRicvJStkZW5vbWFsaWduR1EnY2VudGVyRicvJSludW1hbGlnbkdGX3IvJSliZXZlbGxlZEdGMUYvRlFGMkYvRlFGMi1GIzYmLUZccDYoLUZhcDYmRlxyRi9GUUYyLUYjNiYtRmFwNiZRIjJGJ0YvRlFGMkYvRlFGMkZqcUZdckZgckZickYvRlFGMi8lMXN1cGVyc2NyaXB0c2hpZnRHUSIwRidGL0ZRRjJGKy8lJ2ZhbWlseUdRMFRpbWVzfk5ld35Sb21hbkYnRi9GMg== LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYjLUkjbW9HRiQ2LlEhRicvJStleGVjdXRhYmxlR1EmZmFsc2VGJy8lLG1hdGh2YXJpYW50R1Enbm9ybWFsRicvJSZmZW5jZUdGMS8lKnNlcGFyYXRvckdGMS8lKXN0cmV0Y2h5R0YxLyUqc3ltbWV0cmljR0YxLyUobGFyZ2VvcEdGMS8lLm1vdmFibGVsaW1pdHNHRjEvJSdhY2NlbnRHRjEvJSdsc3BhY2VHUSYwLjBlbUYnLyUncnNwYWNlR0ZF LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYjLUkjbW9HRiQ2LlEhRicvJStleGVjdXRhYmxlR1EmZmFsc2VGJy8lLG1hdGh2YXJpYW50R1Enbm9ybWFsRicvJSZmZW5jZUdGMS8lKnNlcGFyYXRvckdGMS8lKXN0cmV0Y2h5R0YxLyUqc3ltbWV0cmljR0YxLyUobGFyZ2VvcEdGMS8lLm1vdmFibGVsaW1pdHNHRjEvJSdhY2NlbnRHRjEvJSdsc3BhY2VHUSYwLjBlbUYnLyUncnNwYWNlR0ZF gravitational acceleration 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 LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYjLUkjbW9HRiQ2LlEhRicvJStleGVjdXRhYmxlR1EmZmFsc2VGJy8lLG1hdGh2YXJpYW50R1Enbm9ybWFsRicvJSZmZW5jZUdGMS8lKnNlcGFyYXRvckdGMS8lKXN0cmV0Y2h5R0YxLyUqc3ltbWV0cmljR0YxLyUobGFyZ2VvcEdGMS8lLm1vdmFibGVsaW1pdHNHRjEvJSdhY2NlbnRHRjEvJSdsc3BhY2VHUSYwLjBlbUYnLyUncnNwYWNlR0ZF Adiabatic temperature gradient 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 LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYjLUkjbW9HRiQ2LlEhRicvJStleGVjdXRhYmxlR1EmZmFsc2VGJy8lLG1hdGh2YXJpYW50R1Enbm9ybWFsRicvJSZmZW5jZUdGMS8lKnNlcGFyYXRvckdGMS8lKXN0cmV0Y2h5R0YxLyUqc3ltbWV0cmljR0YxLyUobGFyZ2VvcEdGMS8lLm1vdmFibGVsaW1pdHNHRjEvJSdhY2NlbnRHRjEvJSdsc3BhY2VHUSYwLjBlbUYnLyUncnNwYWNlR0ZF Temperature gradient difference 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 Convective velocity 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LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYjLUkjbW9HRiQ2LlEhRicvJStleGVjdXRhYmxlR1EmZmFsc2VGJy8lLG1hdGh2YXJpYW50R1Enbm9ybWFsRicvJSZmZW5jZUdGMS8lKnNlcGFyYXRvckdGMS8lKXN0cmV0Y2h5R0YxLyUqc3ltbWV0cmljR0YxLyUobGFyZ2VvcEdGMS8lLm1vdmFibGVsaW1pdHNHRjEvJSdhY2NlbnRHRjEvJSdsc3BhY2VHUSYwLjBlbUYnLyUncnNwYWNlR0ZF LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYjLUkjbW9HRiQ2LlEhRicvJStleGVjdXRhYmxlR1EmZmFsc2VGJy8lLG1hdGh2YXJpYW50R1Enbm9ybWFsRicvJSZmZW5jZUdGMS8lKnNlcGFyYXRvckdGMS8lKXN0cmV0Y2h5R0YxLyUqc3ltbWV0cmljR0YxLyUobGFyZ2VvcEdGMS8lLm1vdmFibGVsaW1pdHNHRjEvJSdhY2NlbnRHRjEvJSdsc3BhY2VHUSYwLjBlbUYnLyUncnNwYWNlR0ZF
<Text-field style="Heading 1" layout="Heading 1">Solution (A): Central Pressure</Text-field> In order to use the equation of hydrostatic equilibrium to calculate the central pressure of the Sun, it would be necessary to know how the mass and density of the Sun vary with its radius. This is not explicitly known. However, a rough estimate of the central pressure can be obtained from 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 = LV9JLFR5cGVzZXR0aW5nRzYkJSpwcm90ZWN0ZWRHSShfc3lzbGliRzYiSSxtcHJpbnRzbGFzaEdGKDYkNyM+JkkiUEdGKDYjSSJjR0YoLCQqJiQiK2xmI3A1IiIiJyIiIi1JJVVuaXRHNiMvSSdfbG9jYWxHRiZJMF9uMjAxOTIyNzgxMTU1MkdGKDYjSSNQYUc2Iy9GO0kwX24yMDE5MjI4MDYxNDcyR0YoRjZGNjcjLCQqJkYzRjZLSSVVbml0RzYkL0krbW9kdWxlbmFtZUdGKEkmVW5pdHNHRiVGJkY9NiQtSStVbml0U3RydWN0R0ZHNiVGNkkncGFzY2FsRzYkUUpDOlxQcm9ncmFtfkZpbGVzXE1hcGxlfjIwMTdcbGliXG1hcGxlLm1sYUYoL0Y7STBfbjIwMTkyNDk4MzQ2NTZHRihJI1NJRy9GOy9GSUkpY29udGV4dHNHL0Y7L0ZJRk9JJmluZXJ0R0YoRjZGNg== or about 1015 pascals. This is off by a factor of approximately 10 from the currently accepted figure: 2.34 * 1016 pascals, calculated from solar models. (See Appendix, Table 17, in the text.) JSFHJSFH
<Text-field style="Heading 1" layout="Heading 1">Solution (B): Central Temperature</Text-field> The total pressure is related to temperature by 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 where the first term on the right is the pressure due to the ideal gas law, and the second term is the pressure due to radiation. The contribution due to radiation is much smaller than that due to gas pressure, so the second term on the right can be ignored. Since LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYoLUkjbWlHRiQ2JlEjUGNGJy8lJ2l0YWxpY0dRJXRydWVGJy8lK2V4ZWN1dGFibGVHUSZmYWxzZUYnLyUsbWF0aHZhcmlhbnRHUSdpdGFsaWNGJy1JI21vR0YkNi5RIj1GJ0YyL0Y2USdub3JtYWxGJy8lJmZlbmNlR0Y0LyUqc2VwYXJhdG9yR0Y0LyUpc3RyZXRjaHlHRjQvJSpzeW1tZXRyaWNHRjQvJShsYXJnZW9wR0Y0LyUubW92YWJsZWxpbWl0c0dGNC8lJ2FjY2VudEdGNC8lJ2xzcGFjZUdRLDAuMjc3Nzc3OGVtRicvJSdyc3BhY2VHRk4tSSZtZnJhY0dGJDYoLUYjNiotRiw2JlEiR0YnRi9GMkY1LUY5Ni5RJyZzZG90O0YnRjJGPEY+RkBGQkZERkZGSEZKL0ZNUSYwLjBlbUYnL0ZQRmduLUYsNiZRIk1GJ0YvRjJGNUZZLUYsNiZRJiZyaG87RicvRjBGNEYyRjwvJSdmYW1pbHlHUTBUaW1lc35OZXd+Um9tYW5GJ0YyRjwtRiM2Ji1GLDYmUSJyRidGL0YyRjVGYG9GMkY8LyUubGluZXRoaWNrbmVzc0dRIjFGJy8lK2Rlbm9tYWxpZ25HUSdjZW50ZXJGJy8lKW51bWFsaWduR0ZdcC8lKWJldmVsbGVkR0Y0RmBvRjJGPA== the pressure equation can be rewritten as 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 = LV9JLFR5cGVzZXR0aW5nRzYkJSpwcm90ZWN0ZWRHSShfc3lzbGliRzYiSSxtcHJpbnRzbGFzaEdGKDYkNyM+SSJUR0YoLCQqJiQiKy50cUY5ISIjIiIiLUklVW5pdEc2Iy9JJ19sb2NhbEdGJkkwX24yMDE5MjI0NTQzMTY4R0YoNiNJIktHNiMvRjhJMF9uMjAxOTI1MzA4NTE4NEdGKEYzRjM3IywkKiZGMEYzS0klVW5pdEc2JC9JK21vZHVsZW5hbWVHRihJJlVuaXRzR0YlRiZGOjYkLUkrVW5pdFN0cnVjdEdGRDYlRjNJJ2tlbHZpbkc2JFFKQzpcUHJvZ3JhbX5GaWxlc1xNYXBsZX4yMDE3XGxpYlxtYXBsZS5tbGFGKC9GOEkwX24yMDE5MjQ5ODM4OTc2R0YoSSNTSUcvRjgvRkZJKWNvbnRleHRzRy9GOC9GRkZMSSZpbmVydEdGKEYzRjM= The accepted value is 1.55 * 107 kelvins. (See Appendix, Table 17, in the text.) LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYjLUkjbW9HRiQ2LlEhRicvJStleGVjdXRhYmxlR1EmZmFsc2VGJy8lLG1hdGh2YXJpYW50R1Enbm9ybWFsRicvJSZmZW5jZUdGMS8lKnNlcGFyYXRvckdGMS8lKXN0cmV0Y2h5R0YxLyUqc3ltbWV0cmljR0YxLyUobGFyZ2VvcEdGMS8lLm1vdmFibGVsaW1pdHNHRjEvJSdhY2NlbnRHRjEvJSdsc3BhY2VHUSYwLjBlbUYnLyUncnNwYWNlR0ZF
<Text-field style="Heading 1" layout="Heading 1"><Equation executable="true" style="Heading 1" input-equation="" display="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">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</Equation>Solar Pressure Scale Height</Text-field> The pressure scale height, Hp,is an estimate of the size of a convective zone. Using 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 = 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 JSFH 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 = LV9JLFR5cGVzZXR0aW5nRzYkJSpwcm90ZWN0ZWRHSShfc3lzbGliRzYiSSxtcHJpbnRzbGFzaEdGKDYkNyM+JkkiSEdGKDYjSSJwR0YoLCQqJiQiKyFScThBKCEiIiIiIi1JJVVuaXRHNiMvSSdfbG9jYWxHRiZJMF9uMjAxOTI0MDAzMzIxNkdGKDYjSSJtRzYjL0Y7STBfbjIwMTkyNDI4NzkzOTJHRihGNkY2NyMsJComRjNGNktJJVVuaXRHNiQvSSttb2R1bGVuYW1lR0YoSSZVbml0c0dGJUYmRj02JC1JK1VuaXRTdHJ1Y3RHRkc2JUY2SSZtZXRyZUc2JFFKQzpcUHJvZ3JhbX5GaWxlc1xNYXBsZX4yMDE3XGxpYlxtYXBsZS5tbGFGKC9GO0kwX24yMDE5MjQ5ODM3MTIwR0YoSSNTSUcvRjsvRklJKWNvbnRleHRzRy9GOy9GSUZPSSZpbmVydEdGKEY2RjY= A commonly accepted value is 5 * 108 metres (Basu & Antia, 1997).LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYjLUkjbW9HRiQ2LlEhRicvJStleGVjdXRhYmxlR1EmZmFsc2VGJy8lLG1hdGh2YXJpYW50R1Enbm9ybWFsRicvJSZmZW5jZUdGMS8lKnNlcGFyYXRvckdGMS8lKXN0cmV0Y2h5R0YxLyUqc3ltbWV0cmljR0YxLyUobGFyZ2VvcEdGMS8lLm1vdmFibGVsaW1pdHNHRjEvJSdhY2NlbnRHRjEvJSdsc3BhY2VHUSYwLjBlbUYnLyUncnNwYWNlR0ZF
<Text-field style="Heading 1" layout="Heading 1"><Font size="18" style="Heading 3" italic="false">Solution (D); Solar Adiabatic Sound Speed for a Monatomic Gas</Font></Text-field> The sound speed, vs, depends on the compressibility and inertia of the gas. Average solar pressure 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 = LV9JLFR5cGVzZXR0aW5nRzYkJSpwcm90ZWN0ZWRHSShfc3lzbGliRzYiSSxtcHJpbnRzbGFzaEdGKDYkNyM+JkkiUEdGKDYjSSNhdkdGKCwkKiYkIitEKUhZYCYiIiYiIiItSSVVbml0RzYjL0knX2xvY2FsR0YmSTBfbjIwMTkyNDY0OTY4MzJHRig2I0kjUGFHNiMvRjtJMF9uMjAxOTIyODA2MTQ3MkdGKEY2RjY3IywkKiZGM0Y2S0klVW5pdEc2JC9JK21vZHVsZW5hbWVHRihJJlVuaXRzR0YlRiZGPTYkLUkrVW5pdFN0cnVjdEdGRzYlRjZJJ3Bhc2NhbEc2JFFKQzpcUHJvZ3JhbX5GaWxlc1xNYXBsZX4yMDE3XGxpYlxtYXBsZS5tbGFGKC9GO0kwX24yMDE5MjQ5ODM0NjU2R0YoSSNTSUcvRjsvRklJKWNvbnRleHRzRy9GOy9GSUZPSSZpbmVydEdGKEY2RjY= 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 = 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 A typical value of the adiabatic sound speed inside the Sun is 5 * 105 m/s (Bahcall, Basu & Pinsonneault, 1998).
<Text-field style="Heading 1" layout="Heading 1">Solution (E): The Adiabatic Convection by Mixing-Length Theory</Text-field> To calculate values pertaining to the base of the Sun's convection zone, the following values may be used: Gravitational acceleration as the base of the convection zone 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 = LV9JLFR5cGVzZXR0aW5nRzYkJSpwcm90ZWN0ZWRHSShfc3lzbGliRzYiSSxtcHJpbnRzbGFzaEdGKDYkNyM+SSJnR0YoLCQqJiQiKyJIaU5LJiEiKCIiIi1JJVVuaXRHNiMvSSdfbG9jYWxHRiZJMF9uMjAxOTIyMjg4OTM3NkdGKDYjKiZJIm1HNiMvRjhJMF9uMjAxOTI0MjI3MjMyMEdGKEYzKUkic0c2Iy9GOEkwX24yMDE5MjQyMjcyMzg0R0YoIiIjISIiRjNGMzcjLCQqJkYwRjNLSSVVbml0RzYkL0krbW9kdWxlbmFtZUdGKEkmVW5pdHNHRiVGJkY6NiQqJi1JK1VuaXRTdHJ1Y3RHRkw2JUYzSSZtZXRyZUc2JFFKQzpcUHJvZ3JhbX5GaWxlc1xNYXBsZX4yMDE3XGxpYlxtYXBsZS5tbGFGKC9GOEkwX24yMDE5MjQ5ODM3MTIwR0YoSSNTSUcvRjgvRk5JKWNvbnRleHRzRy9GOC9GTkZVRjMtRlM2JUYzSSdzZWNvbmRHNiRGVy9GOEkwX24yMDE5MjQ5ODM3MzEyR0YoSSNTSUc2JEZXL0Y4STBfbjIwMTkyNDk4MzczNzZHRighIiNJJmluZXJ0R0YoRjNGMw== JSFH The adiabatic temperature gradient in the Sun's convective zone is: 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 = 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 JSFH and the temperature gradient difference is 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 LUkmbW92ZXJHNiMvSSttb2R1bGVuYW1lRzYiSSxUeXBlc2V0dGluZ0dJKF9zeXNsaWJHRic2JS1JI21vR0YkNi9RJyZyYXJyO0YnLyUrZXhlY3V0YWJsZUdRJXRydWVGJy8lMGZvbnRfc3R5bGVfbmFtZUdRKDJEfk1hdGhGJy8lLG1hdGh2YXJpYW50R1Enbm9ybWFsRicvJSZmZW5jZUdRJmZhbHNlRicvJSpzZXBhcmF0b3JHRjovJSlzdHJldGNoeUdGMS8lKnN5bW1ldHJpY0dGOi8lKGxhcmdlb3BHRjovJS5tb3ZhYmxlbGltaXRzR0Y6LyUnYWNjZW50R0Y6LyUnbHNwYWNlR1EsMC4yNzc3Nzc4ZW1GJy8lJ3JzcGFjZUdGSS1JJm10ZXh0R0YkNiZRLGF0fjV+ZGlnaXRzRidGL0YyRjVGRQ== evalf[5]( ); 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 LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYjLUkjbW9HRiQ2LlEhRicvJStleGVjdXRhYmxlR1EmZmFsc2VGJy8lLG1hdGh2YXJpYW50R1Enbm9ybWFsRicvJSZmZW5jZUdGMS8lKnNlcGFyYXRvckdGMS8lKXN0cmV0Y2h5R0YxLyUqc3ltbWV0cmljR0YxLyUobGFyZ2VvcEdGMS8lLm1vdmFibGVsaW1pdHNHRjEvJSdhY2NlbnRHRjEvJSdsc3BhY2VHUSYwLjBlbUYnLyUncnNwYWNlR0ZF The ratio of the temperature gradient difference to the adiabatic temperature gradient: 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 = JCIrK0Eib0olISM7 LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYjLUkjbW9HRiQ2LlEhRicvJStleGVjdXRhYmxlR1EmZmFsc2VGJy8lLG1hdGh2YXJpYW50R1Enbm9ybWFsRicvJSZmZW5jZUdGMS8lKnNlcGFyYXRvckdGMS8lKXN0cmV0Y2h5R0YxLyUqc3ltbWV0cmljR0YxLyUobGFyZ2VvcEdGMS8lLm1vdmFibGVsaW1pdHNHRjEvJSdhY2NlbnRHRjEvJSdsc3BhY2VHUSYwLjBlbUYnLyUncnNwYWNlR0ZF LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYjLUkjbW9HRiQ2LlEhRicvJStleGVjdXRhYmxlR1EmZmFsc2VGJy8lLG1hdGh2YXJpYW50R1Enbm9ybWFsRicvJSZmZW5jZUdGMS8lKnNlcGFyYXRvckdGMS8lKXN0cmV0Y2h5R0YxLyUqc3ltbWV0cmljR0YxLyUobGFyZ2VvcEdGMS8lLm1vdmFibGVsaW1pdHNHRjEvJSdhY2NlbnRHRjEvJSdsc3BhY2VHUSYwLjBlbUYnLyUncnNwYWNlR0ZF This is the degree to which the actual temperature gradient is superadiabatic. Therefore, it is possible to regard the temperature gradient deep in the convective zone as being equal to the adiabatic gradient. This greatly simplifies modelling of the convective zone (Mullan, 2010). 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 The convective velocity is about 51 m/s, which is a reasonable estimate (Langer, 2016). This represents 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 = LCQqJiQiKyZRd2daJSEjOSIiIikiIiMjRidGKUYnRic= LUkmbW92ZXJHNiMvSSttb2R1bGVuYW1lRzYiSSxUeXBlc2V0dGluZ0dJKF9zeXNsaWJHRic2JS1JI21vR0YkNi9RJyZyYXJyO0YnLyUrZXhlY3V0YWJsZUdRJXRydWVGJy8lMGZvbnRfc3R5bGVfbmFtZUdRKDJEfk1hdGhGJy8lLG1hdGh2YXJpYW50R1Enbm9ybWFsRicvJSZmZW5jZUdRJmZhbHNlRicvJSpzZXBhcmF0b3JHRjovJSlzdHJldGNoeUdGMS8lKnN5bW1ldHJpY0dGOi8lKGxhcmdlb3BHRjovJS5tb3ZhYmxlbGltaXRzR0Y6LyUnYWNjZW50R0Y6LyUnbHNwYWNlR1EsMC4yNzc3Nzc4ZW1GJy8lJ3JzcGFjZUdGSS1JJm10ZXh0R0YkNiZRLGF0fjV+ZGlnaXRzRidGL0YyRjVGRQ== evalf[5]( ); JCImLEwnISIq approximately 1/10,000 of the sound speed.
<Text-field style="Heading 1" layout="Heading 1">References</Text-field> Bahcall, J., Basu, S. & M. Pinsonneault. (1998). How Uncertain Are Solar Neutrino Predictions? Phys. Lett. B, 433, 1-8. Basu, S. & Antia, H. (1997). Seismic measurement of the depth of the solar convection zone. Mon. Not. R. Astron. Soc. 287, 189-198. Langer, N. (2016). Lecture Notes. https://astro.uni-bonn.de/~nlanger/siu_web/ssescript/new/chapter4-5.pdf (Accessed: 2016-08-25.) Mullan, D. (2010). Physics of the Sun: A First Course. Boca Raton: Taylor and Francis Group.
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