A watt is a derived unit for a rate of change, an amount of energy used in a unit of time, so P = E / t. A kW per hour would be a rate divided by time, or E / t^2, resulting in another rate.
More colloquially, think of watts/power by analogy to another rate, that of speed. Moving at a speed of 100kph for 3 hours results in 300 speed-hours of distance. Saying 100 kilometers per hour per 3 hours sounds awkward, but is actually a weird way to say acceleration, a rate of change of speed. (And probably a hint to get your car serviced.)
Anyway, the key is to think of a kilowatt as a rate, not a quantity.
I see now that watts and therefore kW are rates. So it’s silly to add another rate to the end by appending “per hour”. But what is the time component of the watt calculation? To me it’s essentially instantaneous, even if that’s wrong. Even if that breaks the math, it’s still essentially true on a macro scale. And if it’s instantaneous, or even just close like microseconds, then it doesn’t hurt to apend another rate to the end, does it?
So why not use it? Batteries come with capacities rated in Wh and kWh, and it weirdly still makes sense to me because of my usage rate per hour example in my last comment.
And if we shouldn’t use it, then what should we use?
Is this problem we’re discussing, one that only occurs if you try to get really accurate with the numbers and times? Because for my uses it’s always seemed to work well enough.
Not being argumentative, just trying to learn, thanks
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·m2 / s3. 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·m2 / s2, 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. 😀
A watt is a derived unit for a rate of change, an amount of energy used in a unit of time, so P = E / t. A kW per hour would be a rate divided by time, or E / t^2, resulting in another rate.
More colloquially, think of watts/power by analogy to another rate, that of speed. Moving at a speed of 100kph for 3 hours results in 300 speed-hours of distance. Saying 100 kilometers per hour per 3 hours sounds awkward, but is actually a weird way to say acceleration, a rate of change of speed. (And probably a hint to get your car serviced.)
Anyway, the key is to think of a kilowatt as a rate, not a quantity.
Thanks, I guess I still don’t understand though.
I see now that watts and therefore kW are rates. So it’s silly to add another rate to the end by appending “per hour”. But what is the time component of the watt calculation? To me it’s essentially instantaneous, even if that’s wrong. Even if that breaks the math, it’s still essentially true on a macro scale. And if it’s instantaneous, or even just close like microseconds, then it doesn’t hurt to apend another rate to the end, does it?
So why not use it? Batteries come with capacities rated in Wh and kWh, and it weirdly still makes sense to me because of my usage rate per hour example in my last comment.
And if we shouldn’t use it, then what should we use?
Is this problem we’re discussing, one that only occurs if you try to get really accurate with the numbers and times? Because for my uses it’s always seemed to work well enough.
Not being argumentative, just trying to learn, thanks
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·m2 / s3. 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·m2 / s2, 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. 😀