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Lecture17_CS

# Lecture17_CS - 1 Hydrostatic Equilibrium Quantum Pressure...

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2 Hydrostatic Equilibrium Quantum Pressure Compact Stars Summary
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4 Pressure due to gravity Pressure interior to shell Pressure exterior to shell
5 The gravitational force on the shell is where m ( r ) is the mass enclosed in radius r

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6 The pressure difference Δ p between the interior and exterior of the shell must equal the pressure due to gravity F / A In the limit of infinitely thin shells we have
7 The pressure p (0) in the core is the sum of the pressure differences between all shells, from r = R at the surface to r = 0 at the center

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8 For a constant density ρ (r) = ρ , the core pressure is Using M = 2 x 10 30 kg, R = 7 x 10 8 m for the Sun we find p (0) = 1.3 x 10 14 Pa (1 Pascal = 1 N/m 2 ) A more precise calculation yields 2.3 x 10 16 Pa The pressure at Earth’s surface is ~ 10 5 Pa
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10 The stability of white dwarfs and neutron stars is determined by the balance between the gravitational pressure and the quantum pressure due to electrons and neutrons, respectively, that arises from the Pauli exclusion principle.
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Lecture17_CS - 1 Hydrostatic Equilibrium Quantum Pressure...

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