[firebacon]

"Adding the hour" doesn't make it have "two time components" -- it makes it have no time component.

The joule is a unit of ENERGY.

The watt is a unit of {WORK,POWER}. Confusingly, the germanic languages use "Work" for the concept ("Arbeit" in DE or "Arbeid" in NL), but in English it is "Power". Power means transfer of ENERGY over TIME. Specifically, the Watt it is defined as one Joule per second.

So Watts are a unit of POWER. And POWER=ENERGY/TIME. Note that this is a divison, not a multiplication!

So what do you get by multiplying a Watt by a unit of time (in this case hours)?

  > We're multiplying: WORK * TIME  [Watt * Hour]
  > Which is: (ENERGY/TIME) * TIME  [(Joule/Second) * Hour]
  > And the result is.....: just ENERGY

As you can see, the Watt-Hour is a unit of energy, just like the Joule. There is nothing weird about it.

Hope that could clear things up -- best greetings from the Netherlands!