FWIW, I think you made a minor math error; you lost track of the 30 minutes. It would be 1 ounce of water for 3 watts of power over 30 minutes, which is 1.5 Wh of energy. That's 666 ounces per kWh.
Let me rephrase and use watt/hour units.
I was assuming it was a 50 watt panel that would only produce 30wh from the weak winter sunlight.
Divide 30wh by two (since it was only ru Ning for half an hour) and get 15 watts generated to purify 5 ounces.
Had they let it run for the full hour, they’d get 10 ounces from my assumed 30wh of energy the panel produced.
30wh divided by 10 ounces would be 3wh per ounce (or unit of water produced).
How many units of water can be produced by 1kwh? Let’s divide 1,000wh by 3wh to get the result of 333.3 units (ounces) produced.
In your original post, the number was 15 watts, and you figured it produced 5 ounces of water in 30 minutes. So you then figured that 3 watts can produce 1 ounce of water in 30 minutes. So far so good; that's correct. If the panel continuously produces 3 watts of power (remember: watts are a rate of energy) over a period of one hour, that's 3 watt-hours of energy. For 30 minutes, it's 1.5 watt-hours of energy. Thus, it took 1.5 watt-hours of energy to produce 1 ounce of water. (1000 watt-hours) * (1 ounce / 1.5 watt-hours) = 666 ounces.
It may make more sense to translate this into distance, which I think is more intuitive for most people. Watts (power) are like miles-per-hour (velocity), and watt-hours (energy) are like miles (position). The panel runs at 15 MPH. After 30 minutes it has run 7.5 miles and produced 5 ounces of water. Thus, it could produce 1 ounce of water by running just 1.5 miles. It still runs at a speed of 15 MPH no matter what.
They meant 15 watt-hours in both cases, which would be half of 30 watt-hours — or a 50 watt panel for 30 minutes at 60% efficiency. (Which is the stated working premise.)
15 watt-hours -> 5oz would imply that 3 watt-hours -> 1oz, and hence 1 kWh is 333oz.
I generally try to assume best intentions — so if they repeated otherwise the same correct math, but for misnaming a unit, I try to assume they’re correct and typo’d.
However, I think I’d still make the same mistake in the future because I don’t understand how to express what the (assumed) 50 watt rated panel is generating over half an hour.
If it’s running at 60% efficiency then it’s generating at 30 watts per hour.
After an hour of running, we’ve accumulated 30 watts of energy.
If we only ran it for half hour, we’d have 15 watts.
Dividing that out tells me that 3 watts of energy will provide 1 once of water.
Does it matter if those 3 watts are provided over an hour via a 3wh power source or over 10 minutes via a 16wh power source?
“Watt” is the unit of power which is the rate of change in “joules”, which is the unit of energy. In the way that “velocity” is the rate of change in “position”.
1w = 1J/s
A “watt-hour” is another way to represent joules/energy by integrating watts/power over time.
30 watts * 30 minutes = 15 watt-hours or 54 kJ.
30 miles/hour * 30 minutes = 15 miles or 24km
> Does it matter if those 3 watts are provided over an hour via a 3wh power source or over 10 minutes via a 16wh power source?
You have the units backwards:
You can get 3wh from 1 hr @ 3w or 10 min @ 18w.
So let’s create one: the “walk” is the speed a person can walk — 3mph.
Then I can say the store is “3 walk-hours away”, even if I normally drive the 9 miles with my car.
3 walk-hours = 3 hours @ 1 walk = 18 minutes @ 10 walk (or 30mph)
Batteries are rated in “watt-hours” for the same reason:
3wH = 3 hours @ 1 watt = 18 minutes @ 10 watt
I’m assuming what I’m saying is wrong, I just can’t spot it. Thanks for the help.