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1.M. Graetzel and P. Infelta, The Bases of Chemical Thermodynamics (Universal Publishers/, 2002), Vol. 1, pp. 110116.
2.R. N. O’Brien, C. Forgacs, and J. Schlechter, Chemistry International 3, 24 (1980).
4.M. Turek and B. Bandura, Desalination 205, 67 (2007).
5.J. W. Post, J. Veermanb, H. V. M. Hamelersa, G. J. W. Euverinkb, S. J. Metzb, K. Nymeijerc, and C. J. N. Buisman, J. Membr. Sci. 288, 218 (2007).
6.To be precise, saturated hydrocarbons in diesel fuel have a H/C ratio of slightly more than 2.1, but diesel fuel often contains alkenes from catalytic cracking, reducing the H/C ratio.
7.The enthalpy of combustion is based on the higher heating value of 45.5 MJ/kg (heat released by combustion of diesel fuel with condensation of water vapor), expressed per mole of fuel.
8.The term can be rearranged in the form , where , and then simplified by applying the relationship , which applies in the limit as U approaches zero.

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One potential source of useful energy that seems to be unrecognized and overlooked is the “entropy of mixing” of engine exhaust gases with the atmosphere. In particular, exhaust gases from combustion engines typically contain carbon dioxide at concentrations 250 times greater than in the atmosphere and have an oxygen concentration that is typically less than one-tenth the oxygen concentration in the atmosphere. Fuel cell power sources can produce exhaust gases containing concentrations 1000 times greater than in the air. Currently, engine exhaust gases are simply ejected into the atmosphere where they spontaneously mix with the air, and the potential to do useful work is lost. Rather than discarding combustion gases into the atmosphere, it is possible—in principle—to exploit the entropy of mixing to produce useful work. However, the energy that could potentially be produced by mixing exhaust gases with air is at least an order of magnitude less than the energy released by combustion of the fuel. Exploiting this energy source is likely to prove difficult and expensive with current technology, but ultimately, this “mixing energy” could be an incremental energy source to be finessed from combustion engines, kilns, furnaces, and fuel cell power sources. This article proposes conceptual designs for “mixing engines” that could augment the power output of a diesel engine by as much as 3.0% or augment the power output of a fuel cell power plant by 3.5%.


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