So, bocijn and Zeus46 admit they can't do arithmetic. OK I can deal with that.
bocijn keeps asking for the error in the excess power, Excess power is computed by subtracting input power from the (measured) output power. Thus the POE equation is:
(s_Pex)^2 = (s_Pout)^2 + (s_Pin)^2 (simple since the partials of Pex w.r.t Pin and Pout are -1 and 1, respectively, which bo and Zeus could not compute either).
So, now we need to choose our confidence level (the number of 'sigmas' we will consider. I prefer 5.
Next we need to decide how much error was in the calibration constant. Let's go with what Miles has reported for his work, which essentially agrees with what Storms reported and I confirmed, 1% (that's the magnitude of 1 standard deviation).
So that means the s_Pout we will use will be 5 * .01 * measured Pout (which coincidentally will be nearly exactly Pin, go figure...), which is 5 * .01 * 134 = 6.7W.
Now that minimizes the error, since we could have used 5 or 10% (which will give 33.5 and 67W bands respectively (bo and Zeus, work this out for yourselves as practice).
For simplicity here, we will note that the authors report an error of 0.031W in Pin, which is considerably smaller and means we can ignore it. We thereby slightly underestimate the error in Pex, but not too badly since it is a factor of 100 or so under the Pout error, i. e. 100*0.031/134 = 0.023% error (try working out this calc bo and Zeus as arithmetic practice), almost two orders of magnitude better than that in Pout. However, we all note that 6.7 W is *NOT* the 0.26W the authors report. Hmmm...wonder how that happened... (This illustrates the typical occurrence in CF work, where the errors are significantly underestimated, thereby allowing CF researchers to feel they are not 'working in the noise, which we all know is a sign of pathological science.)
Now don't forget that the authors used Tave to simplify their calorimetric equation by claiming fixed values of the density and specific gravity. I previously calculated the 200-300 degree range they reported led to, what was it, 8 and 13% error spreads? You can check back to the post where I did that if you need to. But that means you need to add terms into the error equation for those variables. But we can just guess they are equal to the cal constant term (a conservative estimate) and end up (proof left to readers, use this to practice your arithmetic) with the 6.7W error being increased to 11.6W. That['s the error in Pex bo and Zeus. So that means any excess power under roughly 11-12W is 'in the noise' and shouldn't be trusted. Since that error was calculated conservatively, just for safety you might want it multiply it by 5 or 10 (can you do that by yourselves?).