I think there's a big question of how Naudin measures the input power, given that his input is pulsed. He doesn't explicitly say how he measures it.
http://www.gifnet.ch/lab/mahg/mahg2d.htm Suppose you have a pulsed DC source connected to a resistor. Vp = peak voltage Va = average voltage R = resistance Ip = peak current Ia = average current Pp = peak power Pa = average power Po = thermal power output d = duty cycle, less than or equal to 1 Then Pp = (Vp^2) / R ( ^ is exponentiation) Pa = d * (Vp^2) / R ( * is multiplication) Po = Pa Va = d * Vp Ip = Vp / R Ia = d * (Vp / R) Now suppose someone thinks that you can measure the average power by multiplying the average voltage times the average current. Let's call this Pf (f for fake or false). Pf = Va * Ia = d^2 * (Vp^2) / R Pf = d * Pa Pf = d * Po If the duty cycle is the 5% that Naudin uses, the fake average input power is only 5% of the actual average input power. And if the increase in water heat measured by calorimetry is due solely to resistive heating, i.e., Po = Pa -- the output power equals the true average input power -- then the output power divided by the fake average input power would equal 1/d. In other words, if COP means output power divided by input power (I can't find an actual definition of COP on the Web), then COPf = fake COP = Po / Pf = 1/d For Naudin's 5% duty cycle, the fake COP would be 20. He measures about 21.
