UNIVERSE (LOOSELEAF):STARS+GALAXIES
UNIVERSE (LOOSELEAF):STARS+GALAXIES
6th Edition
ISBN: 9781319115043
Author: Freedman
Publisher: MAC HIGHER
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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
Check Mark

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
Check Mark

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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