General
Prefixes
10
deka(da) 10-1
deci(di)
102
hecto(h) 10-2
centi(c)
103
kilo(k) 10-3
milli(m)
106
mega(M) 10-6
micro(m)
109
giga(G) 10-9
nano(n)
1012 tera(T) 10-12 pico(p)
1015 peta(P) 10-15 femto(f)
1018 exa(E) 10-18 atto(a)
Conversions
1 year
= 3.1536E7 seconds
1
joule = 1 kg m2/sec2 = 1 newton-meter
1
joule = 1 watt-second (Ws)
3.6E6
joules = 1 kWh
1
pascal = 1 N/m2 = 1 J/m3
1
newton (N) = 1 kg m/sec2
Stefan-Boltzmann (s) = 5.669E-8 J/(m2-K4-sec)
A = 6.02E23 molecules/mole
Ideal
Gas (R) = 8.310 J/mole-K
Speed
of light (c) = 2.9979E8 m/sec
Gravitation (G) = 6.67E-11 N-m2/kg2
Acceleration
= 9.8 m/sec2
Earth
Mass
Earth = 5.98E24 kg
Mass
Atm = 5.14E18 kg
Mass
Strat = 0.5E18 kg
Mass
Oceans = 1.4E21 kg
Mass
water in Atm = 1.3E16 kg
Mass
surface fresh water = 1.26E17
Mass
living org (dry) = 1.3E15
Moles
dry air in atm = 1.8E20
p(atm)
= ½ @ 5600 m
Top
trop = 12,000 m
Mean
ocean depth = 3,730 m
Mixed
layer = 75 m
Cont.
Elev. = 840 m
Earth
Area = 5.10E14 m2
Cont.
= 1.48E14 m2
Ocean Area = 3.61E14 m2
Ocean Volume = 1.35E18 m3
Ocean mixed-layer = 2.7E16 m3
Earth
Density = 5500 kg/m3
Surface
seawater density = 1,026 kg/m3
Mean
surface air temp = 288 K
Astronomical
EarthÛSun = 1.495E11 m
Earth Radius = 6.38E6, polar 6.36
Sun
Radius = 6.96E8 m
Sun Mass = 1.99E30 kg
EarthÛMoon = 3.84E8
Moon Radius = 1.74E6 m
Moon Mass = 7.34E22 kg
Lunar revolution = 2.36E6 sec
Nucleons in the universe = 1080
Radius of universe = 1026 m
Air
28.96
g/mole; 22.4 l/mole
specific
heat = 1,004.2 J/kg oC
Density
= 1.293 kg/m3
Conductivity
= 0.0209 W/m oC
Molecule Moles Mass
N2 0.7808 0.7549
O2 0.2095 0.2314
Ar 0.0093 0.0128
CO2 370 ppm 516 ppm
He 5.2 ppm 0.7 ppm
H2 0.5 ppm 0.03 ppm
N2O 0.3 ppm 0.45 ppm
O3 0.01 ppm 0.015 ppm
NO2
0.2 ppb 0.3 ppb
SO2 0.2 ppb 0.4 ppb
H2S 0.05 ppb 0.05 ppb
NO 0.05 ppb 0.05 ppb
NH3 0.05 ppb 0.03 ppb
Water
0 999.87 kg/m3
3.98 1,000 kg/m3
25 997.07 kg/m3
Latent
heat Fusion @ 0 = 3.33E5 J/kg; 79.6 cal/g
Latent
heat vapor. @100= 2.258E6 J/kg; 539.6 cal/g
@
17 = 2.459E6 J/kg
Specific
heat of liquid water @ 15 = 4,184 J/kg oC
Specific
heat water vapor @ 100 = 2,008.3 J/kg oC
Coefficient
heat conductivity @ 17 = 0.595 W/m oC
Stocks of Water (1015
m3)
Oceans
1,350
Ice 29
Groundwater 8.3
Fresh
lakes 0.125
Saline
lakes 0.104
Soil 0.067
Atmosphere
0.013
Biomass 0.003
Rivers 0.001
Flows of water (1012 m3/yr)
World precip. Land 108
In sea 410
Et land 62
Et sea 456
Runoff 46
Energy (1012
W)
Sun radiates 3.7E14
Solar
radiation top atm 175,000(343)
Reflected
back from earth 53,000
Reflected
back from atm 46,000
Solar
radiation in atm 44,000
Latent
heat earthàatm 42,000
IR
earthà space 10,200
Convection
surf à atm 8,600
Ocean
currents ~1250
NPP 100
Geoà earth surface 30
World
energy con 10(2.5)
Food 0.55
Electricity 0.87
(1E6 J/kg)
Dry biomass 16
Wood 15
Fat 38
Gas 48
Oil 43
Coal 29.3
Reaction 10-pK
H2O
Û H+ + OH- 10-14
H2CO3
Û H+ + HCO3- 10-6.35
HCO3-
Û H+ + CO3-2 10-10.33
HCl Û
H+ + Cl- 103.0
H2SO4
Û H+ + HSO4- 103.0
HSO3-
Û H+ + SO3-2 10-1.9
HNO3 Û H+ + NO3-1 103.0
H2SO3
Û H+ + HSO3- 10-1.77
HSO3-
Û H+ + SO3-2 10-7.21
NH3 + H2O Û NH4+ + OH- 10-4.74
H3BO3
Û H+ + H2BO3- 10-9.3
Equilibrium
ratio KH
(moles/liter-atm)
[H2SO3]/p(SO2) 100.096
[H2CO3]/p(CO2) 10-1.47
[HNO3]/p(NO2) 10-1.6
[NH3]/p(NH3) 101.76
[CO]/p(CO) 10-3.0
[N2O]/p(N2O) 10-1.59
[H2S]/p(H2S) 10-0.97
Solid solubility product (moles2/liter2)
Calcite [Ca+2][CO3-2]
= 10-8.42
Aragonite [Ca+2][CO3-2]
= 10-8.22
[Ca+2][CO3-2]
= 10-6.05 seawater
gypsum [Ca+2][SO4-2]
= 10-4.6
dolomite [Ca+2][Mg+2][CO3-2]2
= 10-16.7
Reaction Constant
(liters/mole)
2H+ + CuO Û Cu+2 + H2O 107.7
3H+ + Al(OH)3 Û Al+3 + 3H2O 108.5
Biomass Living Dead NPP
(1012 kg (C)) (1012 kg
(C)/yr)
Cont. 560 1500 50
Marine 2 2,000 25
Wood C:N Ratio 200:1
Biomass C:N Ratio 10:1
Biomass H20O10C10N
Ecosystem
type area biomass NPP
1012
m2 kg(c)/m2 per year
Tropical
forests 24.5 18.8 0.83
Temperate
forests 12 14.6 0.56
Boreal
forests 12 9 0.36
Woodland 8 2.7 0.27
Savanna 15 1.8 0.32
Grassland 9 0.7 0.23
Tundra 8 0.3 0.065
Desert 18 0.3 0.032
Rock,
ice 24 0.01 0.015
Cultivated
land 14 0.5 0.29
Swamp 2 6.8 1.13
Lake
and stream 2.5 0.01 0.23
Ocean 332 0.0014 0.057
Upwelling
zones 0.4 0.01 0.23
Cont.
shelf 26.2 0.005 0.16
Algal
bed and reef 0.6 0.9 0.9
Estuaries 1.4 0.45 0.81
Resulting formula:
σ Ts4 =
3Ω(1-a)/4 – [Fc + 1.5Fe +1.7Fs + 2Fw]
Fc = 17 w/m2 (convective
heat flow)
Fe = 80 w/m2 (latent
heat)
Fs = 86 w/m2 (absorbed
in atm)
Fw = 20 w/m2 (radiated
to space)
Ts = temperature of the surface
To = first, lower layer
T1 = second, higher layer
The 2 is the two-layer system
The 3 is n layers + 1
Empirically we know that this energy gets
dumped in the lower troposphere. Most
of the water is in the lower atmosphere.
Ω/4 = 343 w/m2
a = 0.3
p166
W + W/4 = a(W/4
) + sTo4 + Fw
2sTo4 = sT14
+ 0.5Fe + 0.7Fs
2sT14 = sTo4
+ sTs4 – Fw + Fc
+ 0.5Fe + 0.3Fs + W
sTo4 =
220.1 W/m2; To = 249.6 K
sT14 = 340 W/m2; T1 = 278.3
K
sTs4 =
397.1 W/m2; Ts = 289.3 K
Fin
(p) = pollutant flow, mass/time
Fin
(water) = water flow, mass/time
Concentration
in lake is Mp/Mwater
dM(water)/dt
= 0; Fin (water) = Fout (water)
twater = Mwater/Fin,water
t(p) = Mp/Fout,p
(only applies when Fin, p = Fout, p)
Proceed,
assuming Steady-state
Fout,
p = Mp/Mw*(Fout, w)
In
other words, Fout, p = concentration * total outflow
tp = Mp/[Mp/Mw * (Fout,w)] =
Mw/Fout, w = twater (only applies at steady
state.
Additionally,
if Et applied, tp would be > twater
General equation
dMp/dt
= Fin, p – Mp/Mw * (Fout, w)
Of
the general form, dx/dt = a –bx; a linear, donor-controlled equation.
Mp(t)
= Mp(0) + [twater*Fin,p –
Mp(0)][1-e-t/twater]
tà0, Mp(0) = Mp(0) + [twater * Fp,in –Mp(0)]*[0]
tà¥, Mp(¥)
= Mp(0) + [twater * Fp,in –Mp(0)]*[1]
Mp(¥)
= twater * Fp,in (this only applies
when there is no evaporative loss of water and tp = twater)
In
general at SS, Mp(¥) = tp*Fp,in
Another
approach for steady state situations,
dMp/dt
= Fin, p – Mp/twater
0 =
Fin, p – Mp/twater
Mp =
Fin, p * twater, essentially applies because
we know tp = twater
