Quote:
Originally Posted by Besoeker
Actually, it does not accord with any equations. Energy can not be instantaneous.
I think maybe therein is the crux of the matter.
Call the period or passage of time p.
For 0<p<1 as you suggest, p is a finite value. It could, for example, 0.5s, that being the passage of time. That isn't instantaneous.
Going back to your comment in post #35
"Fundamentally speaking, a unit of power (Watt) is equivalent to a unit of energy (Joule) over a unit of time (Second)"
That gives us:
W=J/s
And that gives us the more fundamental definition:
Power is the RATE of doing work. It could be Nm/s, ft-lbf/s, kW etc.
(That applies whether it is electrical, mechanical, or fluid power.)
The rate of doing work.
Energy is what you get from that rate of work over a period of time. No time, no energy.
One kWh can be generated in an hour, a week, or 1ms (1ms being 3.6GW)
But not instantaneously.
An analogy that may be helpful......
Suppose that you drive at a rate of 60kph.
Travel for an hour you do 60km
In a minute, 1km
In a second, 17m
In 1ms, 17mm.
In other words, the rate at which you travel (instantaneous speed) tells you nothing about the distance you will cover unless you define time period. You can't instantly cover 50m.
|
That above description is somewhat misleading. Instantaneous speed is not simply the rate at which you travel. Instantaneous speed is the speed or rate of travel at a given moment or instant in time. The rate at which you travel is simply distance over time.
Getting back to the main point though, if energy cannot be instantaneous, then nor can power, because power without time is meaningless. Power requires time to have meaning. Instantaneous implies in an instant with no intervening time, making time zero and if time is zero then work cant be done and if work cant be done then power does not exist.
Power is a rate at which work is performed or the amount of energy expended over a unit of time. This rate is a ratio, in which two measurements ( 1. unit of energy - joule and 2. time ) are related to each other to derive meaning. If no time passes then this rate cannot exist, yet to be instantaneous requires no passing of time, meaning time is zero, therefore power cannot exist if time is zero. Power W requires 1 joule over 1 second. If time does not pass then power does not exist and thus cannot be derived. If no work is done then power does not exist. For work to be done time must pass. i.e. for 1 unit of work being 1 joule, 1 second must pass. However, to be instantaneous requires no passing of time. We thus have a null contradiction.
However for descriptive purposes in terms of measuring energy over a very short space of time a different interpretation of instantaneous is sometimes given. i.e. without perceptible time. This might explain one reason why in fact the term instantaneous energy is used in areas of science and technology.
It's clearly not pragmatic to have zero time, meaning without passing of time, or no intervening time, because this would mean zero energy, zero work done and zero power. Thus pragmatically speaking, instantaneous time is applied to simply mean, a very short space of time and usually sub-second but greater than zero time. i.e. for pragmatic purposes no perceptible time, being a very short space of time.
Regardless of all this though, it does not change the fact that the intended meaning of the articles is clear.