The simple answer is that Watts are already a measurement of rate.
1Watt = 1Joule/ Sec
So a watt-second is a count of energy
Joule/Sec * Sec = just Joules
A watt per second is like a measurement of acceleration – how “fast” is my rate changing?
Watt/Sec = Joules/Sec/Sec.
Using hours is just saying “3600 seconds” in the above math.
Think of it like “mph”, if mph was it’s own unit.
1mph * 1hour = 1 mile.
1mph/1hour = I sped up from 50 mph to 51 mph over the course of an hour.
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