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GEOG/ENVS 4201, Biometeorology, Fall 2009
Tues/Thurs 12:15 - 1:45, GUGG 205 
Worksheets

# 1 - Radiation Basics             [Questions | Answers ]
# 2 - Effective Temperature    [Questions | Answers ]
# 3 - Water Potential
#1 Questions
  1. Calculate the energy emitted at each of the surface temperatures (To) and wavelengths (l):

a)      6000 K;     0.5 um

b)      5000 K;     400 nm

c)      20 oC;        20 um

d)      75 oF;         8 x 10-6 m

  1. Calculate the wavelength of maximum energy emission for the blackbody objects at the following To:

a)      0 oC

b)      -40 oF

c)      300 K

d)      6000 K

  1. Calculate the total energy emitted (all wavelengths) for objects with the following To and emissivities (e):

a)      0 oC;          0.98

b)      300 K;       0.90

c)      0 oF;           1.00

d)      25 oC;        0.99

#1 Answers

Constants
c = 3e8;                speed of light m s^-1
h = 6.63e-34          Planck's constant J s
k = 1.38e-23          Boltzmann constant J K^-1
sigma = 5.67e-8    Stefan-Boltzmann constant W m^-2 K^-4
w_c = 2897           Wien's constant um K^-4

1. ALL T MUST BE IN K; ALL WAVE LENGTH MUST BE IN m TO GIVE E IN W m^-2 m^-1

a)
T = 6000; wave = 0.5/1e6;
E = 2*pi*h*c^2./(wave^5.*(exp(h*c/(wave*k*T))-1)) = 9.9119e+013

b)
T = 5000; wave = 400/1e9;
E = 2*pi*h*c^2./(wave^5.*(exp(h*c/(wave*k*T))-1)) = 2.7177e+013

c)
T = 20 + 273.15; wave = 0.5/1e6;
E = 2*pi*h*c^2./(wave^5.*(exp(h*c/(wave*k*T))-1)) = 2.7177e+013

d)
T = (5/9)*(75-32) + 273.15; wave = 8e-6;
E = 2*pi*h*c^2./(wave^5.*(exp(h*c/(wave*k*T))-1)) =  2.6630e+007

2. USE T in KELVIN to give max. wavelength in um

a)    0 oC
T = 0 + 273.15;
l_max = w_c./T = 10.6059

b)    -40 oF
T =  (5/9)*(-40-32) + 273.15;
l_max = w_c./T = 12.4255

c)    300 K
T = 300;
l_max = w_c./T = 9.6567

d)    6000 K
T = 6000
l_max = w_c./T =  0.4828

3. USE T in KELVIN to give E in W m^-2

a)    0 oC;     0.98
T = 0 + 273.15;
E = 0.98*sigma*T^4 = 309.3242

b)    300 K;     0.90
T = 300;
E = 0.90*sigma*T^4 = 413.3430

c)    0 oF;     1.00
T = (5/9)*(0-32) + 273.15;
E = 1.00*sigma*T^4 =  241.1447

d)    25 oC;     0.99
T = 25 + 273.15;
E = 0.99*sigma*T^4  =  443.5652

 ------ end worksheet #1 answers ----------
Worksheet #2 Questions

Calculate the effective temperature for a person under each of the following conditions:


  1. A sunny, calm, humid day:

 

Absorbed Radiation:                             800 W m-2

Air Temperature:                                  30 deg C

Surface Emissivity:                                0.98

Radiative Conductance:                        0.22 mol m-2 s-1

Boundary Layer Conductance:  0.46 mol m-2 s-1

Specific Heat:                                       29.3 J mol-1 C-1

 

 

  1. A sunny, windy, dry day:

 

Absorbed Radiation:                             800 W m-2

Air Temperature:                                  30 deg C

Surface Emissivity:                                0.98

Radiative Conductance:                        0.22 mol m-2 s-1

Boundary Layer Conductance:  1.45 mol m-2 s-1

Specific Heat:                                       29.3 J mol-1 C-1

 

  1. A cloudy, calm, humid day:

 

Absorbed Radiation:                             400 W m-2

Air Temperature:                                  20 deg C

Surface Emissivity:                                0.98

Radiative Conductance:                        0.20 mol m-2 s-1

Boundary Layer Conductance:  0.46 mol m-2 s-1

Specific Heat:                                       29.3 J mol-1 C-1

 

  1. A very cloudy, windy, humid day:

 

Absorbed Radiation:                             200 W m-2

Air Temperature:                                  20 deg C

Surface Emissivity:                                0.98

Radiative Conductance:                        0.20 mol m-2 s-1

Boundary Layer Conductance:  1.45 mol m-2 s-1

Specific Heat:                                       29.3 J mol-1 C-1

#2 Answers
Answers (all deg C):

 

  1. 46.6
  2. 36.8
  3. 19.8
  4. 15.6

Worksheet #3 – Water Potential

1.      Calculate the volumetric water content for each of the following:

Total Material Volume (cm3)

Liquid Water Volume (cm3)

Volumetric Water Content

(cm3 H2O cm3 material)

50

2

 

137

89

 

200

98

 

239

139

 

 

2.      Calculate the gravimetric water content for each of the following:

Material Dry Mass (g)

Liquid Water Mass (g)

Gravimetric Water Content

(g H2O g dry material)

10

50

 

87

123

 

232

400

 

345

525

 

 

3.      Calculate the gravitational water potential  for each of the following:

Height above reference plane (m)

Liquid Water Density (kg m3)

Gravitational Water Potential

(Pa)

0

1000

 

2

999

 

5

998

 

100

1000

 

 

 4.      Calculate the soil matric water potential for each of the following:

Gravimetric Water Content

(g H2O g dry material)

Soil Matric Water Potential

(Pa)

0.10

 

0.50

 

0.75

 

0.90

 

 

 5.      Calculate the pressure water potential for each of the following (use 1000 kg m-3 for water density):

Internal Pressure (Pa)

Atmospheric Pressure (Pa)

Pressure Water Potential

(Pa)

70,000

100,000

 

80,000

90,000

 

100,000

85,000

 

80,000

80,000

 

 

6.      Calculate the osmotic water potential for each of the following (use 300 K and treat as an ideal solute for all):

Solute

Solute Concentration (mole kg-1)

Osmotic Water Potential

(Pa)

NaCl

0.5

 

KCl

0.3

 

CaCO3

0.2

 

CO2

0.1

 

 

7.      Calculate the air  water potential for each of the following :

Relative Humidity

Temperature (K)

Air Water Potential

(Pa)

0.90

290

 

0.85

300

 

0.40

273

 

0.75

285

 

 



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