Universe: Stars And Galaxies
Universe: Stars And Galaxies
6th Edition
ISBN: 9781319115098
Author: Roger Freedman, Robert Geller, William J. Kaufmann
Publisher: W. H. Freeman
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Chapter 20, Problem 30Q
To determine

(a)

The average density of the 1M white dwarf having the same diameter as Earth.

Expert Solution
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Answer to Problem 30Q

The density of the 1M white dwarf having the same diameter as Earth is 1.84×109kgm-3.

Explanation of Solution

Given:

The diameter of the1Mwhite dwarf=Earth's diameter=12,756km

Mass of the white dwarf=2×1030kg

Formula used:

Density of a material can be determined by the formula,

Density=massvolume

Volume of a sphere is given by the formula,

Volume of a sphere=43π(D2)3

Where; D=diameter of the white dwarf in meters

Calculation:

Density= 2×10 30kg43×3.14× ( 12,756km 2 )3=1.84×109kgm-3

Conclusion:

The density of the white dwarf having the same radius as Earth is 1.84×109kgm-3.

To determine

(b)

To check: Whether the density of one teaspoon full of 1M white dwarf matter is same as the density of an elephant.

Expert Solution
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Answer to Problem 30Q

The mass of one teaspoon of the white dwarf matter is about 9,000kg; nearly as the mass of an African male elephant. Therefore, the white dwarf has the density of about one elephant per teaspoon.

Explanation of Solution

Given:

Volumeof a tea spoon=4.92ml=4.92cm3

density of the white dwarf=1.84×109kgm-3

Mass of an average elephant(African male)7,000kg

Formula used:

Mass of a material can be determined by the formula,

mass=Density×volume

Calculation:

mass=1.84×109kgm-3×4.92×10-6m3=9,052.8kg

Conclusion:

The mass of one teaspoon of the white dwarf matter is about 9,000kg; nearly as the mass of an African male elephant. Therefore, the white dwarf has the density of about one elephant per teaspoon.

To determine

(c)

Speed required for a gas to escape the surface of the white dwarf.

Expert Solution
Check Mark

Answer to Problem 30Q

The speed required to eject a gas from the surface of the white dwarf is 6,469kms1.

Explanation of Solution

Given data:

(gravitational constant)=6.673×10-11m3kg-1s-2

Mass of the white dwarf(Mwd)=2×1030kg

Radiusofthewhite dwarf=6,378×103m

Let Vesc be the escape speed from the white dwarf,

Formula used:

Escape speed is given by the formula,

Vesc=2GM wdR wd

Where; Vesc=escape velocityG=gravitational constantMwd=mass of the white dwarfRwd=radius of the white dwarf

Calculation:

Vesc1= 2×6 .673×10 -11 m 3 kg -1 s -2 ×2×10 30 kg 6,378,000m=6,469,166.08ms-16,469kms-1

Conclusion:

The speed required to eject a gas from the surface of the white dwarf is 6,469kms-1.

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