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[Phys-l] Thermodynamics and Energetic Residence Time in Ecology and Engineering

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.

[17] US Energy Information Administration, Carbon Dioxide Emissions from the Generation of Electric Power in the United States
(accessed January 8, 2010)

Above text was excerpted from the following:

Jeff Radtke, Supersaturated Environments