Question

A white dwarf is a star that has exhausted its nuclear fuel and lost its outer mass so that it consists only of its dense, hot inner core. It will cool unless it gains mass from some nearby star. It can form a binary system with such a star and gradually gain mass up to the limit of 1.4 times the mass of the Sun. If the white dwarf were to start to exceed the limit, it would explode into a supernova. How much energy is released by the explosion of a white dwarf at its limiting mass if $80.0 \%$ of its mass is converted to energy?

Name: Problem 41, Chapter 26: Physics
Uploaded: 2020-05-23T19:01:53-08:00
Duration: 1 min 58 s
Channel: Dading Chen

   A white dwarf is a star that has exhausted its nuclear fuel and lost its outer mass so that it consists only of its dense, hot inner core. It will cool unless it gains mass from some nearby star. It can form a binary system with such a star and gradually gain mass up to the limit of 1.4 times the mass of the Sun. If the white dwarf were to start to exceed the limit, it would explode into a supernova. How much energy is released by the explosion of a white dwarf at its limiting mass if $80.0 \%$ of its mass is converted to energy?

Physics

Alan Giambattista,… 2nd Edition

Chapter 26, Problem 41

Instant Answer

Solved by Expert Dading Chen

05/23/2020

Step 1

Step 1: We know that the energy released by a mass converting to energy is given by Einstein's equation, $E=mc^2$, where $E$ is the energy, $m$ is the mass, and $c$ is the speed of light. Show more…

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A white dwarf is a star that has exhausted its nuclear fuel and lost its outer mass so that it consists only of its dense, hot inner core. It will cool unless it gains mass from some nearby star. It can form a binary system with such a star and gradually gain mass up to the limit of 1.4 times the mass of the Sun. If the white dwarf were to start to exceed the limit, it would explode into a supernova. How much energy is released by the explosion of a white dwarf at its limiting mass if $80.0 \%$ of its mass is converted to energy?

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Key Concepts

White Dwarf

A white dwarf is the dense remnant of a star that has exhausted its nuclear fuel. It represents the final evolutionary stage for stars with mass similar to or less than that of the Sun, where the outer layers are ejected and only the hot, degenerate core remains.

Chandrasekhar Limit

The Chandrasekhar limit is the maximum mass (approximately 1.4 times the mass of the Sun) that a white dwarf can have while remaining stable. Beyond this limit, the electron degeneracy pressure that supports the white dwarf against gravitational collapse is overcome, leading to further collapse or thermonuclear explosion.

Mass–Energy Equivalence

Mass–energy equivalence is a fundamental concept in physics encapsulated by Einstein's equation E = mc², which states that mass can be converted into energy and vice versa. In astrophysical phenomena like the explosion of a white dwarf, a portion of the mass is transformed into an enormous amount of energy.

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