Problems
611
Here, we take R E = 6.371 × 10 6 m; R E−S = 150 × 10 9 m; α = 0.3; ε = 0.77;
T sun = 5778 K. The above gives an effective radiation temperature of the Earth
as T Earth = 18 ◦ C. A better calculation would include the radiative energy flow
from the Earth’s atmosphere and surface, taking account the atmospheric spectral
absorption and emission in each layer above the Earth, and give an effective
temperature of 15 ◦ C.
16.2 The Negentropy of Life
The Earth not only has a flux of energy from the Sun and a nearly equal amount of
energy expelled into outer space, it also has a flow of solar entropy in and a flow
of entropy out. Although energy is conserved, entropy is not. The rate of entropy
out is much larger than that coming in from the Sun, while the open geological and
life systems become more ordered. The reduction of entropy of open subsystems is
measured by ‘negentropy’, i.e. its loss of entropy, which Shannon has shown is a
form of information storage in that subsystem.
The entropy flow from the Sun to the Earth is given by (4/3)P sun /T sun . The
entropy flow into space from the Earth is (4/3)P Earth /T space . (The factors 4/3 =
1 + 1/3 include 1/3 to account for the entropy generated by the dissipation of the
work done by the pressure of light.) Thus the net entropy flow is
dS
dt
≥
4
3
P Earth
T space
−
P sun
T sun
=
4
3
P Earth
1
T space
−
1
T sun
> 0 .
(16.3)
In the above, the radiation temperature of outer space is T space = 2.76 K. Since
T sun >> T space , the entropy flow into outer space from the Earth must exceed
the flow in from the Sun. The production of entropy in the Universe by the
Earth allows subsystems, including life systems on Earth, to reduce in entropy,
up to the rate given in Eq. (16.3). This ordering process can be in the formation
of complex molecules, chemical energy storage, and the utilization of work for
transport processes.
Problems
16.1 Under what conditions would the activity of life benefit from periods of stasis,
suspended animation, hibernation, and stagnation?
16.2 If energy flow can be controlled by an evolving system, what factors might
determine an optimal flow?
611
Here, we take R E = 6.371 × 10 6 m; R E−S = 150 × 10 9 m; α = 0.3; ε = 0.77;
T sun = 5778 K. The above gives an effective radiation temperature of the Earth
as T Earth = 18 ◦ C. A better calculation would include the radiative energy flow
from the Earth’s atmosphere and surface, taking account the atmospheric spectral
absorption and emission in each layer above the Earth, and give an effective
temperature of 15 ◦ C.
16.2 The Negentropy of Life
The Earth not only has a flux of energy from the Sun and a nearly equal amount of
energy expelled into outer space, it also has a flow of solar entropy in and a flow
of entropy out. Although energy is conserved, entropy is not. The rate of entropy
out is much larger than that coming in from the Sun, while the open geological and
life systems become more ordered. The reduction of entropy of open subsystems is
measured by ‘negentropy’, i.e. its loss of entropy, which Shannon has shown is a
form of information storage in that subsystem.
The entropy flow from the Sun to the Earth is given by (4/3)P sun /T sun . The
entropy flow into space from the Earth is (4/3)P Earth /T space . (The factors 4/3 =
1 + 1/3 include 1/3 to account for the entropy generated by the dissipation of the
work done by the pressure of light.) Thus the net entropy flow is
dS
dt
≥
4
3
P Earth
T space
−
P sun
T sun
=
4
3
P Earth
1
T space
−
1
T sun
> 0 .
(16.3)
In the above, the radiation temperature of outer space is T space = 2.76 K. Since
T sun >> T space , the entropy flow into outer space from the Earth must exceed
the flow in from the Sun. The production of entropy in the Universe by the
Earth allows subsystems, including life systems on Earth, to reduce in entropy,
up to the rate given in Eq. (16.3). This ordering process can be in the formation
of complex molecules, chemical energy storage, and the utilization of work for
transport processes.
Problems
16.1 Under what conditions would the activity of life benefit from periods of stasis,
suspended animation, hibernation, and stagnation?
16.2 If energy flow can be controlled by an evolving system, what factors might
determine an optimal flow?