Tuesday, February 12, 2013
I hit on this before with the Golden Efficiency. The work portion of any cycle is likely limited to 38% percent. So let's imagine that Q is 500 Watts. If we have our 38% then W in the first stage might be 190 Watts and S, for entropy might be 410 Watts. With up to 410 Watts available for stage 2, W could equal 156 Watts and S could be 254 Watts. With a third stage, W could be 96 Watts and S equal 157 Watts. Since I have the Work arrows pointing in two directions, we could have 190/2 plus 156/2 plus 96/2 = 95+78+48=221 Watts for our three stage fan in two dimensions.
Since the efficiency of each stage is not likely to be the same and since each depends on the other, we could end up with a little instability. If we know the maximum efficiency of each stage though, we can work with the design to determine a range of possibilities and what might be the larger thing that impact the efficiency of each stage.
It does starting getting complicated though. Which is why I tend to look at energy period instead of this or that energy. So if I use just Watts for Q, we can consider these stages just heat engines and don't bother dusting off the steam tables. That requires a little better estimate of Q. With the tropical oceans having a peak temperature or roughly 30C and a latent heat of cooling in the range of 90 Wm-2, we can use the Stefan-Boltzmann equivalent energy for 30C of 478 Wm-2 and ~90Wm-2 for a Q of 568Wm-2
We would have to be careful with our units, but when the total work is equal to the final entropy, we would be in the ballpark of a stable system. In other words, when internal transfer is equal to external loss there would be 50% efficiency for the combined system which might meet the maximum/minimum entropy required for a stable open system.
Just a different way of looking at things.