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tiL12214_appe_643-698.indd Page 692 09/10/10 8:37 AM user-f463
tiL12214_appe_643-698.indd Page 692 09/10/10 8:37 AM user-f463 Volume/207/MHDQ243/tiL12214_disk1of1/0073512214/tiL12214_pagefile

radiation by the reflected solar radiation to determine the absorbed energy = At (insolation − reflected solar radiation)

albedo, denoted by alpha.
Convert hours to seconds:
3 W _
incoming solar radiation = 1.37 × 10 _ 60 s

60 min _
(
)(
m 2 1 h 1 h 1 min )

( 3 W _ 2)
reflected solar radiation = 20% 1.37 × 10 360 s

m
1 W _
2 W _
(
2)
2

2 W _ absorbed energy = 1.5 m (360 s) 7.3 × 10 −8.8 × 10

= 2.74 × 10 m 2 m
m 2
2 W _
2)
(
2
α = ? = 1.5 m (360 s) 6.4 × 10

__ m
reflected solar radiation

α =

incoming solar radiation _ J s _

2
2
2 W _ = 1.5 (360)(6.4 × 10 ) m (s) ( )

2.74 × 10 m 2
2
m

5

= __ = 3.5 × 10 J
3 W _
1.37 × 10

m 2
Step 3: Determine the Mass of Asphalt
W _
2
m _
2
_
2.74 × 10 m _ 2 A = 1.5 m ρ = and V = zA ∴ m = ρ zA

= 3 W _ V

1.37 × 10 z = 5.0 cm
m 2 _ m = ρ zA
g

= 0.2 ρ = 2.3
3
cm Convert m to cm :
2
2
22.11. Use the average lapse rate of −6.5°C/1,000 m to determine the m = ?
(
_
4
2 1 × 10 cm 2

summit temperature. 1.5 m 2 )

1 m
4
T sea level = 25°C T summit = T sea level + z summit (lapse rate) 1.5 × 10 cm 2
)
(
z summit = 4,169 m = 25°C + 4,169 m _ _ 4 2
−6.5 °C
g

_ 1,000 m m = 2.3 (1.5 × 10 cm )(5.0 cm)
−6.5°C
3
cm
lapse rate =

1,000 m _ °C _ g
)
(
−6.5
_

= 25°C + 4,169 m ( ) = 2.3(1.5 × 10 )(5.0) (cm )(cm)

4
2

T summit = ? 1,000 m cm 3
= 25°C + (−27 °C) = 1.7 × 10 g
5
= −2°C
Step 4: Determine Temperature Change of Asphalt
22.12. Subdivide the problem into smaller steps that consider The energy can then be used with the specific heat equations in

the amount of incoming solar radiation reflected back into chapter 4 to determine the change in temperature of the
the atmosphere, the energy transferred to the asphalt from the asphalt. The relationship between heat, the mass of the asphalt,

incoming solar radiation, and the warming of the soil that and the temperature change is equation 4.4 in chapter 4.
would occur as a result of this energy.
5
m = 1.7 × 10 g _
Q

Step 1: Determine Reflected Radiation _ Q = mc ΔT ∴ ΔT =
mc
cal

The albedo is used to determine the amount of solar radiation c = 0.22 g⋅°C ___

4
(8.3 × 10 cal)

reflected back into the atmosphere. Th e reflected solar radiation energy = 3.5 × 10 J ΔT = 5 _

5
(
cal

is the product of the albedo and the insolation. (1.7 × 10 g) 0.22 g⋅°C)
Convert energy to calorie heat:
2 W _ 4
(cal)
(8.3 × 10 )

insolation = 7.3 × 10 = __ _

5 _
(
)

m 2 Q = 3.5 × 10 J 1 cal (1.7 × 10 )(0.22) _

( g⋅°C)
5
cal

α = 0.12 4 4.184 J (g)
reflected solar radiation = ? = 8.3 × 10 cal
ΔT = ? = 2.2 °C
__
reflected solar radiation

α =
insolation 22.13. Subdivide the problem into smaller steps that consider the
∴ reflected solar radiation = insolation (α) amount of incoming solar radiation reflected back into the

2 W _ atmosphere, the energy transferred to the sand from the
reflected solar radiation = 7.3 × 10 (0.12)

m 2 incoming solar radiation, and the warming of the sand that
1 W _ would occur as a result of this energy.
= 8.8 × 10

m 2
Step 1: Determine Reflected Radiation
Step 2: Determine Energy The albedo is used to determine the amount of solar radiation

The energy from the absorbed solar radiation, in joules, is the area reflected back into the atmosphere. Th e reflected solar radiation

(A) of the layer of asphalt times the time (t) in seconds times the is the product of the albedo and the insolation.

difference between the insolation and the reflected solar radiation.

2 W _
Insolation = 8.7 × 10

2 W _ m 2

insolation = 7.3 × 10
m 2 α = 0.4
1 W _ reflected solar radiation = ?

reflected solar radiation = 8.8 × 10
m 2
A = 1.5 m 2
t = 1 h
absorbed energy = ?
692 APPENDIX E Solutions for Group A Parallel Exercises E-50