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14.9. Determine the brightness of the Sun on Mars, and rearrange Referring to Table 14.2, this would be a type K star that is
the equation provided to determine the area of the solar panel orange-red.
array necessary to produce 10 kW at an efficiency of 40 percent.

14.12. T = 7,000 K
Determine the brightness of the Sun on Mars:
λ peak = ?
26
L
L Sun = 4 × 10 W B = _ 7

__
11
d = 2.3 × 10 m 4πd 2 T = 2.897 × 10 K ⋅ angstrom

B = ? __ λ peak
26
4 × 10 W
7
= _ 1 _ 2.897 × 10 K ⋅ angstrom _ 1 _

__
λ peak
λ peak
11

4π(2.3 × 10 m) 2 × × T = × ×

1 T λ peak 1 T
26
4 × 10
__ W _ 2.897 × 10 K ⋅ angstrom
7

= __

11 2
4π(2.3 × 10 ) m 2 λ peak = T
7
26
4 × 10
_ W _ 2.897 × 10 K ⋅ angstrom
= = __

6.6 × 10 23 m 2 7,000 K
7
_ _
2 W _ 2.897 × 10 K ⋅ angstrom
= 6 × 10 =

m 2 7,000 K
3
= 4.14 × 10 angstroms
Rearrange the equation to solve for area required to generate

10 kW of electricity at an efficiency of 40 percent. 14.13. Determine the temperature of the star from Figure 14.8.
According to this figure, the temperature of Betelgeuse

P required = 10 kW P required = (efficiency) BA is 3,000 K.
efficiency = 0.4 1 _ 1 _
2 W _ × P required = 0.4BA × T = 3,000 K
0.4B

B = 6 × 10 0.4B
m 2 λ peak = ?
7
A = ? A = _ 2.897 × 10 K ⋅ angstrom
P required
__

0.4B T =
λ peak
7
_
__
1 _
1 _
Convert the power to watts. _ × × T = 2.897 × 10 K ⋅ angstrom × ×
λ peak
λ peak

1 T λ peak 1 T
1,000W
_ ) 7

P required = 10 kW ( 2.897 × 10 K ⋅ angstrom
__

1 kW λ peak =
T
( )
_ ) _ 7
1,000
W

= 10 ( kW 2.897 × 10 K ⋅ angstrom

1 kW = __

3,000 K
4
= 1 × 10 W
2.897 × 10 K ⋅ angstrom
7
_ _

=

Solve the rearranged equation. 3,000 K
3
= 9.7 × 10 angstrom
4
__
1 × 10 W

A = = 9,700 angstrom

(
2 W _
2)

0.4 6 × 10
m
14.14. Determine the change in the radius of the expanding cloud
4
_
_ W
1 × 10
= over the time period from 1999 to 2008; then use the result to

2
2)
( solve for speed.
0.4(6 × 10 ) _
W

m
1
12
= 4 × 10 m 2 d 1999 = 8.8 × 10 km
13
= 40 m 2 d 2008 = 1.4 × 10 km
Δ radius = ?
7
14.10. λ peak = 6,550 angstroms 2.897 × 10 K ⋅ angstrom
__

T =

T = ? λ peak _
d 2008 − d 1999
Δ radius =

7
2.897 × 10 K ⋅ angstrom 2
__

= 13 12
6,550 angstroms ___
1.4 × 10 km − 8.8 × 10 km

= 2
7
2.897 × 10 K ⋅ angstrom
_ _

= 12
6,550 angstrom _
5.2 × 10

= km

2
3
= 4.42 × 10 K = 2.6 × 10 km
12

14.11. Determine the temperature of the star and then refer to Then divide the change in radius by the elapsed time to
Table 14.2 to determine its type. determine the speed of the gases in the expanding cloud.
12
7
λ peak = 6,050 angstroms __ Δ radius = 2.6 × 10 km _
2.897 × 10 K ⋅ angstrom
Δ radius

T = v =

T = ? λ peak t = 9 yr t 12
2.6 × 10 km
7

2.897 × 10 K ⋅ angstrom
__ v = ? = __

= 9 yr
6,050 angstroms
12
2.6 × 10 _
_ km

2.897 × 10 K ⋅ angstrom
7
_ _ = 9
yr

=

6,050 angstrom 11 km
_

3
yr
= 4.79 × 10 K = 2.9 × 10
= 4,790 K
670 APPENDIX E Solutions for Group A Parallel Exercises E-28