EBK LOOSE-LEAF VERSION OF UNIVERSE
EBK LOOSE-LEAF VERSION OF UNIVERSE
11th Edition
ISBN: 9781319227975
Author: KAUFMANN
Publisher: VST
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Chapter 5, Problem 26Q

(a)

To determine

The energy flux at the surface of Sirius, if the bright star Sirius in the constellation of Canis Major has a radius of 1.67 R.

(a)

Expert Solution
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Answer to Problem 26Q

Solution:

5.75×108 W/m2

Explanation of Solution

Given data:

The bright star Sirius in the constellation of Canis Major has a radius of 1.67 R.

The luminosity is 25 L.

Formula used:

Write the expression for energy flux of the Sun’s luminosity (F).

F=L4πr2

Here, F is energy flux of the Sun’s luminosity or the solar constant or the flux of sunlight, L is the luminosity of the Sun and r is the distance from the Sun to the Earth.

Explanation:

Recall the expression for energy flux of the Sun’s luminosity (F).

F=L4πr2

The bright star Sirius in the constellation of Canis Major has a radius of 1.67 R. Therefore,

R=1.67 RRR=11.67

The luminosity is about 25 L. Therefore,

L=25 LLL=25

The relation between flux and luminosity of the different stars is:

FF=LLR2R2

Substitute 11.67 for RR and 25 for LL.

FF=25(11.67)2=8.96F=8.96F

Refer to Box 5-2 for the value of the energy flux of the Sun’s luminosity.

F=6.41×107 W/m2

Substitute 6.41×107 W/m2 for F.

F=8.96(6.41×107 W/m2)=5.75×108 W/m2

Conclusion:

The energy flux at the surface of Sirius is 5.75×108 W/m2.

(b)

To determine

The surface temperature of Sirius. Also compare the value with that given in Box 5-2, if the bright star Sirius in the constellation of Canis Major has a radius of 1.67 R.

(b)

Expert Solution
Check Mark

Answer to Problem 26Q

Solution:

100035 K; it is very high as compared to the surface temperature of the Sun.

Explanation of Solution

Given data:

The bright star Sirius in the constellation of Canis Major has a radius of 1.67 R.

The luminosity is 25 L.

Formula used:

The expression for Stefan Boltzmann law is:

F=σT4

Here, T is the temperature of the object, F is the energy flux per square unit per second and σ is the Stefan constant (5.67×108 Wm2K4).

Explanation:

Recall the result of part (a).

5.75×108 W/m2

The expression for Stefan Boltzmann law is:

F=σT4

Substitute 5.75×108 W/m2 for F and 5.67×108 Wm2K4 for σ.

5.75×108 W/m2=(5.67×108 Wm2K4)T4T=(5.75×108 W/m25.67×108 Wm2K4)14T=100035 K

Refer to Box 5-2 for the value of the surface temperature of the Sun.

T=5800 K

The surface temperature of Sirius is very high as compared to the surface temperature of the Sun.

Conclusion:

The surface temperature of Sirius is 100035 K and it is very high as compared to the surface temperature of the Sun.

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