Universe
Universe
11th Edition
ISBN: 9781319039448
Author: Robert Geller, Roger Freedman, William J. Kaufmann
Publisher: W. H. Freeman
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Chapter 16, Problem 9Q

(a)

To determine

The time for which the sun must shine in order to release energy produced by the mass-energy conversion of a carbon atom with mass 2×1026 kg. The sun’s luminosity is 3.90×1026 W.

(a)

Expert Solution
Check Mark

Answer to Problem 9Q

Solution:

4.6×1036 s

Explanation of Solution

Given data:

The sun’s luminosity is 3.90×1026 W, and the mass of carbon atom is 2×1026 kg.

Formula used:

Time taken in seconds is given as:

t=EL

Here, E is the energy released due to mass-energy equivalence in joule and L is the luminosity in joule per second.

Einstein’s mass-energy conversion:

E=mc2

Where, E is the energy release from the mass of m and c is speed of light.

Explanation:

Calculating the energy released mass-energy conversion of a carbon atom:

E=mc2

Replace 2×1026 kg for m and 3×108m/s2 for c in the above equation:

E=(2×1026kg)(3×108m/s2)2=1.8×109J

Recalling the expression for time:

t=EL

Substituting 1.8×109 J for E and 3.90×1026 W for L in the above expression:

t=1.8×109 J3.90×1026 Jsecond =4.6×1036 seconds

Conclusion:

The sun must shine 4.6×1036 s to produce the energy produced by a carbon atom with mass 2×1026 kg.

(b)

To determine

The time for which the sun must shine in order to release energy produced by the mass-energy conversion of 1 kg substance. The sun’s luminosity is 3.90×1026 W.

(b)

Expert Solution
Check Mark

Answer to Problem 9Q

Solution:

2.3×1010 s

Explanation of Solution

Given data:

The sun’s luminosity is 3.90×1026 W, and the mass of the substance is 1 kg.

Formula used:

Time taken in seconds is given as:

t=EL

Here, E is the energy released due to mass-energy equivalence in joule and L is the luminosity in joule per second.

Einstein’s mass-energy conversion:

E=mc2

Where, E is the energy release from the mass of m and c is speed of light.

Explanation:

Calculating the energy released mass-energy conversion of a carbon atom:

E=mc2

Replace 1 kg for m and 3×108m/s2 for c in the above equation:

E=(1kg)(3×108m/s2)2=9×1016J

Recalling the expression for the time:

t=EL

Substituting 9.1×1016 J for E and 3.90×1026 W for L in the above expression:

t=9.1×1016 J 3.90×1026 Jsecond =2.3×1010 seconds

Conclusion:

The sun must shine for 2.3×1010 seconds to produce the energy produced by a substance with mass 1 kg.

(c)

To determine

The time for which the sun must shine in order to release energy, produced by the mass-energy conversion of Earth with mass 6×1024 kg. The sun’s luminosity is 3.90×1026 W.

(c)

Expert Solution
Check Mark

Answer to Problem 9Q

Solution:

1.4×1015 seconds

Explanation of Solution

Given data:

The sun’s luminosity is 3.90×1026 W, and the mass of Earth is 6×1024 kg.

Formula used:

Time taken in seconds is given as:

t=EL

Here, E is the energy released due to mass-energy equivalence in joule and L is the luminosity in joule per second.

Einstein’s mass-energy conversion:

E=mc2

Where, E is the energy release from the mass of m and c is speed of light.

Explanation:

Calculating the energy released mass-energy conversion of a carbon atom:

E=mc2

Replace 6×1024 kg for m and 3×108m/s2 for c in the above equation:

E=(6×1024 kg)(3×108m/s2)2=5.4×1041J

Recalling the expression for time:

t=EL

Substituting 5.4×1041 J for E and 3.90×1026 W for L in the above expression:

t=5.4×1041 J3.90×1026 Jsecond =1.4×1015 seconds

Conclusion:

The sun must shine for 1.4×1015 seconds to produce the energy produced by a substance with mass 6×1024 kg.

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