During my water electrolysis with NaOH, I measured the voltage and current, and the volume of gases (hydrogen and oxygen) displaced at every 30-second interval. 10g NaOH in 2L water for 8 minutes.
Then, I was able to calculate the rate of reaction of the gases in terms of volume per unit time. Dividing the rate of reaction by power gives the efficiency of the trial (how much oxygen or hydrogen are produced per unit energy). As I vary the voltage from 5V to 10V and then to 15V, there is a decline in efficiency (less gases produced for each joule).
What is the reasoning for this? My hypothesis is that while the rate of production is directly proportional to current, as I increase the voltage, both current and voltage increases which causes the power to increase at a quicker rate. Ex. $P=IV$, then we increase $V$ to 2$V$, $I$ therefore increases to 2$I$ due to $V=IR$. Therefore $4P=2I \cdot 2V$ where the rate of reaction only increases by a factor of 2. Or is energy lost to heat? But this will not fully account for the large decline as shown in the following picture.