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Kilowatt-hour versus kilowatt per hour

  1. Mar 4, 2012 #1
    My professor asked the cost of running a hair dryer of 1500 W for 15.0 minutes for 5 days a week for 4 weeks. The utility company charged $0.60 per kWh.

    Instinctively, i thought to combine 1500 W with the 15.0 minutes into my version of "kilowatt per hour".

    [tex]1500 W * \frac{1 KW}{1000 W} = 1.50 kW[/tex]
    [tex]1.50 min * \frac{1 hr}{60 minutes} = 0.25 hr[/tex]

    [tex]\frac{1.50 kW}{0.25 hr} = 6 kW/hr[/tex]

    The dryer was used 5 times a week for 4 weeks... so it was used 20 times in the 4 weeks.
    [tex]6 kW/hr * 20 = 120 kW/hr[/tex]

    At... $0.60 per kWh
    [tex]120 kWh * 0.60 \frac{$}{kWh} = $72[/tex]

    The answer was $4.5 not $72. Therefore, my concept of kWh is clearly wrong.

    Can someone explain to me what kWh is intuitively? It clearly is not the amount of kW consumed in an hour.

    Thanks in advance!
  2. jcsd
  3. Mar 4, 2012 #2
    when you pay your bills you pay for the energy you use.The Joule is an inconvenient unit to use for this purpose because it is too small*.Instead the energy unit we use is the kilowatt hour(not kW per hour).The kilowatt hour is literally the number of kilowatts times the number of hours.

    (*one kilowatt hour is 3,600,000Joules.That costs $0.60)
    Last edited: Mar 4, 2012
  4. Mar 4, 2012 #3


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    hi rainstom07! :smile:
    it's (exactly) like man-hours! :wink:

    if 5 men take 4 hours to dig a hole, that's 20 man-hours of work done

    "man" in "man-hours" means manpower (think of horsepower!)

    kWh is power times time, and the "energy company" charges for energy, ie for work done

    watts is power, power is work per time, so energy is work is power times time …

    joules = W times s = kW times h/3,600,000 :smile:
  5. Mar 5, 2012 #4
    A joule is simply an amount of energy. A (kilo) watt is power, or how fast you are using that energy. It is energy divided by time (energy/ time).

    When you multiply this by an hour (to get kilowatt hours), you are multiplying it by a unit of time again. When you multiply (energy/ time) * time, the time actually ends up cancelling out, and all you are left with is energy again.

    So essentially a kilowatt hour is a unit of energy. 1 kilowatt hour = 3,600,000 joules.
  6. Mar 5, 2012 #5

    jim hardy

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    perhaps your concept of a KW isn't quite right. It's a rate of energy use, not an amount of energy.
    Remember heat is energy, and so is mechanical work .
    The unit of energy is the "joule" and that's the work of one newton pushing through one meter. Rub your hands together and feel the warmth of Force X Distance......
    When you're procucing that warmth at the rate of one joule per second you are making one watt - that's what a watt is, one joule per second.
    (I would guess that rubbing your hands together makes on the order of one watt.)

    So a KW is a thousand joules per second;
    ..and a KW-Second would be a thousand joules
    ....and a KW-Hour would be 3600 KW-Seconds, 3.6 million joules.
    Thet's enough heat to evaporate a little more than three pounds water. Or to dry maybe four beautiful heads of hair?

    I hope that helps you 'feel' it.
  7. Mar 5, 2012 #6
    Kilowatt-hour means running a device that uses kW of power for an hour, if you run the device for half an hour, you use 0,5 kW/h, for two hours 2 kW/h etc. A 2 kW device uses 2 kw/h per hour, only 1 kw/h if you run it for half an hour etc.

    You made a mistake in this step:

    If you run a 1,5 kW device for 0,25 hours, it doesn't use 6 kW/h, it is not possible. Even if you run it for an hour, it would use 1,5 kW/h. You need to multiply 1,5 and 0,25 together to get the kw/h per one usage.
  8. Mar 5, 2012 #7


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    KW/hr has no meaning. It is just the way that the uninformed sometimes write kWh.
    Watts is Joules per second. I.e. power is energy per unit time.

    Saying kW/hr is like saying "energy per second per second" - a rate of power Increase. Barmy.
  9. Mar 5, 2012 #8


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    An example of this might the power ramp up rate of some power generating station. For example, a station that can generate 1 milllion kilowatts, but from a cold start, takes 4 hours to reach maximum power generation with a linear ramp up rate of 250,000 kilowatts per hour.

    As sophiecentaur suggested, it's more likely that someone meant kilowatt x hour, or 3.6 million Joules as already posted, as opposed to kilowatt per hour.
    Last edited: Mar 5, 2012
  10. Mar 5, 2012 #9


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    A "kilowatt per hour" is not a 'unit of electricity' or an 'electrical unit' - it is just a rate of change of power.

    There can be similar confusion when talking of battery capacity - Amp Hour Capacity is used, rather than Coulombs, because it is a useful 'size' for a unit. An Amp Second (Coulomb) is too small for most purposes.
    I have heard of people mis-using the term "Amps per Hour" for capacity.
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