The watt is the unit of power, which is the rate at which energy is transferred or transformed. One watt is one joule per second; the joule is the standard unit of energy but is awkwardly small for most real-world measurements. A kilowatt-hour is the amount of energy transferred, when energy is transferred at a rate of one thousand watts over an hour - a much larger and more useful unit of energy. So the device transfers energy at a rate of 15 kilowatts, but only does so for 1/3 of an hour, so it has transferred 5 kWh.
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