N
T
= N
0
• 2
(T/g)
N
T
is the number of cells at time T
N
0
is the number of cells at time T = 0
g is the generation time
as time increases, t/g = 1, 2, 3 ..., thus 2
1
, 2
2
, 2
3
, etc.
A cube has a surface area of 6 • x
2
.
Its volume is x
3
.
For a sphere, the surface area is 4 • π • r
2
, and the volume is π • r
3
.
For a cylinder, the surface area is 2 • π • r • h (plus 2πr
2
for the top and bottom of the
cylinder), the volume is π • r
2
• h.
For a rectangle, the surface area is 2(d•w) + 2(l•d) + 2(l•w), the volume is d•w•l.
Heat conduction rates are defined by the relation:
P
cond
= Q / t = k • A • [(T
a
 T
b
) / L]
where P
cond
is the rate of conduction (transferred heat, Q, divided by time, t); k is the
thermal conductivity;
T
a
and T
b
are the temperatures of the two heat reservoirs a and
b; A is the area; and L is the distance. Thermal conductivities of water and air are
about 0.6 and 0024 W m
–1
K
–1
, respectively.
Thermal radiation is defined by the relation:
P
rad
=
σ • ε
• A • T
4
where P
rad
is the rate of radiation;
σ
is the StefanBoltzmann constant (5.6703 • 10
–8
W
m
–2
K
–4
;
ε
is the emissivity (varies from 0 to 1 for a blackbody radiator); A is the area;
and T is the temperature (in Kelvins). The
net
radiative emission or absorption will
depend upon the difference in temperature:
P
net
=
σ • ε
• A • (T
4
body
– T
4
ambient
)
dM
dt
= μ
M
μ
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 Fall '10
 StanislawJerzakandRogerR.Lew
 Trigraph, Black body, RT ln⎜

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