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 Subject: RE: COP vs Efficiency (and MEG replication) Date: Mon, 14 Jul 2003 19:25:49 -0500   Dear Jim,   Glad you are having some success; please keep at it.   Efficiency is defined as the total useful output (energy or work) divided by the total energy input.   COP is defined as the total useful output (energy or work) divided by only that energy input that the operator furnishes. It specifically does not consider any extra energy the active environment may input.   The solar cell takes all its energy from its active external environment, the solar radiation.  For a typical cell, it wastes about 83% of the input energy, and only outputs 17% as much electrical energy into the circuit as was input to it in the sunlight.  Hence its efficiency is rigorously 17%.   However, the operator inputs ZERO.  Well, to calculate the COP, you place the output (some finite number W, for a real cell) in the numerator and the ZERO input by the operator in the denominator.  COP = W/0 = infinity.  It is perfectly normal to have a system taking all its energy from its external environment, having an efficiency below 50%, and still having COP = infinity. The windmill is one, the sailboat is another, and the waterwheel is another.  All have efficiencies at about 50% or less, but also have COPs of infinity. You need to change your thinking so you clearly understand that no system has more than 100% efficiency, but it can jolly well have COP>1.0 or even COP = infinity, and that DOES NOT violate thermodynamics.   I brought this out because 90% of the electrical engineers do not understand it. Even a few physicists do not understand it.   We also try to give a little more science background, and point out that technically the solar cell thermodynamically is a nonequilibrium steady state (NESS) system.  There is a fairly well-developed thermodynamics of such systems already known and utilized; Prigogine received the Nobel Prize in 1977, e.g., because of his contributions to the thermodynamics of systems far from equilibrium.    And yes, such systems are permitted to do several marvelous things.  They can (i) self-order, (ii) self-oscillate or self-rotate, (iii) output more energy than the operator inputs (the excess is freely received from the external environment), (iv) output real energy that does real work freely, without any operator input (all the energy is freely input from the environment), and (v) exhibit negative entropy.   Item (iv) is that COP = infinity area. Item (iii) is that 1.0