Oh, hey, Jerboa is not so good about updating the Inbox tally…
I was responding to your question about kW per hour, and I was going for the intuitive sense of why that’s not right. The more “it’s just so” reason is that the math just doesn’t work, since the word “per” signifies division. So if we discharge a battery at a rate of 100 watts for 3 hours, that’s 100W * 3 hours, or 300 Wh used. If we say 100 watts per hour for three hours, that’s 100W / 1 hour * 3 hours. The hours cancel, and the result is 300 watts, which is a rate.
It’s totally confusing, I know, because people often use “watts” and “watt-hours” interchangeably, but they’re as different as speed and position.
Anyway, the watt is a derived unit in SI, and it’s equivalent to kg·m^2^ / s^3^. The per-unit-time is hidden when you write it as a watt, but clearly there when you write it in terms of base units. Of course, the joule is kg·m^2^ / s^2^, so energy also has time in the denominator, and I guess could technically also be a rate, but understanding that is way above my pay grade. 😀