Thermodynamics and Energetic Residence Time in Ecology and Engineering
The application of residence time to energy is familiar to ecologists.
This is usually expressed as the ratio of potential energy (as
biomass) to the rate of solar energy input or energy production in the
form of biomass growth. Both terms may be consistently expressed per
unit area for a given biome, an individual organism, or a group.
Ulanowicz and Hannon [16] note the following:
"There appear to be good reasons for believing that the time energy
spends within an ecological system is a key indicator of the degree of
maturity of the system. Both succession and evolution appear to favor
the development of species that retain captured energy for
progressively longer periods."
Engineers and physicists have not adopted residence time as a tool for
understanding energy utilization. This may be because, as Ulanowicz
and Hannon point out, thermodynamics as currently practiced is
unconcerned with how much time energy is in a "compartment." More
specifically, calculations of Carnot cycle efficiency assume that
processes are isothermal or adiabatic and therefore reversible. Such
conditions may only be approached as a limit, given infinite time.
There is a legitimate debate as to whether time belongs in a
thermodynamic theory. The results herein show that energy utilization
studies benefit from consideration of energetic residence time,
suggesting that time may indeed have a place in a more complete
thermodynamics. A final impediment to adoption may be that energy
flow as a colloquial term suffers from connotations with
pseudo-scientific "new age" claims regarding human well-being.
As previously shown, energetic residence time is a valid
transportation system performance metric. A further application of
energetic residence time is as a measure of thermal air conditioning
system performance. For example, suppose it takes 1 kW of
electricity, powering a ground source heat pump, to maintain a 32
cubic meter shed at 20 degrees C, with an outdoor temperature of zero
degrees. The residence time of primary energy in the air filling the
shed is the ratio of the net thermal energy maintained in the air to
the thermal power required to produce 1 kW of electricity. This is
approximately 600,000 Joule divided by 3000 Watts. Or about 200
seconds. Done carefully, this measure accounts for the energy return
on investment to obtain the coal, thermodynamic efficiency at the
powerplant, transmission line losses, heat pump efficiency and
building insulation effectiveness. This is a very complex system, and
energetic residence time is a simple tool for ranking performance.
A scientific consensus has emerged that the available space for carbon
dioxide in the atmosphere has some limit, beyond which human life on
earth will become increasingly intolerable. Since this pollution is
also key to human comfort at our present level of technology, a
performance metric is needed which consistently expresses human
benefit derived from carbon dioxide emission. Such a metric is
available in the energetic residence time of primary fossil fuel
energy as either payload kinetic energy or thermally conditioned air.
It is possible to go a step further along these lines and calculate
the residence time of the energy derived from a molecule of carbon
dioxide emitted. Such a comparison would account for differences in
the ratio of carbon to hydrogen in the fuel. Building on the heating
example described above, suppose the electricity is produced using
thermal energy from some combination of nuclear, hydroelectric,
natural gas, oil and coal sources. If the ratios of energy derived
from these sources, along with respective thermodynamic efficiencies
is known, and average mass of carbon dioxide emitted per Joule can be
calculated. This work has been completed, and the average CO2
emissions per kWhr of electricity generated in the US in 1999 was 0.61
kg.[17] This is the same as a CO2 mass flow rate of 0.17 grams per
second per kW of delivered electrical power.
The numerator should also be expressed in units associated with CO2.
The free energy of formation of CO2 is 94.45 kcal/gram-mole. The
molecular weight of CO2 is 44 grams, so the free energy of formation
is about 9000 J/gram. Kinetic or thermal energy may be expressed in
grams of CO2 formation. The difference in thermal energy content
between heated and unheated air in the above example is equivalent to
the energy of formation of 67 grams of CO2.
So, assuming a circa 1999 average US electrical grid, the energetic
residence time on a per carbon dioxide molecule basis in the heating
example is 67 grams divided by 0.17 grams per second, or about 390
seconds.
This final number tells how effectively CO2 emissions were leveraged.
The 190 second difference between the two residence times indicates
primarily the atmospheric benefits derived from burning hydrogen in
fossil fuels and splitting uranium atoms. Further, comparative
studies including EROI will allow cost/benefit ranking of
comprehensive energy strategies which integrate both production and
conservation measures.
[16] Ulanowicz, R. and Hannon, B. Proc. R. Soc. Lond. B, 232, 1987, 181-192.