2.1.5: Energy expressed in terms of power

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The Watt and its derivatives \((1 \mathrm{~kW}=1000 \mathrm{~W} ; 1 \mathrm{MW}=\) one million Watts; or one miliWatt \(=1 \mathrm{~mW}=0.001 \mathrm{~W})\) are familiar and often, used units. The notion of power readily appeals to one's imagnination. If you hear someone says: "This is a \(60 \mathrm{~W}\) light bulb", or "I have purchased a new \(10 \mathrm{~kW}\) air conditioner for my house ", or "The power of the new Conda Civic's engine is \(150 \mathrm{~kW}\) ", you usually know immediately what this person is talking about.

In contrast, the Joule is a "much more abstract" unit. If one says: "This light bulb has consumed 216000 Joules of energy", you have to think for a moment or even longer to figure out what the person is talking about. Even though it's simple a 60 W bulb uses 60 Joules every second, so over one hour it used \(60 \mathrm{~J} / \mathrm{s} \times 3600 \mathrm{~s}=216000\) Joules.

Therefore, convenient way of describing energy transfer is not to use Joules, but an equivalent unit based on the Watt, called "Watt second", with the symbol Ws, W-s, or W.s. One Watt-second is the amount of energy delivered by a source of \(1 \mathrm{~W}\) power over the period of 1 second so, it's indeed the same as 1 Joule. A derivative unit is the Watt-hour, Wh or W-h, equal to 3600 Joules; and perhaps the most often used energy unit in everyday life, the kiloWatthour, \(\mathrm{kWh}=\) the energy delivered by a source of \(1 \mathrm{~kW}\) power over the period of one hour \(=3,600,000 \mathrm{~J}\).

Look at the bill the power company sends to you you pay for kiloWatthours, not for Joules. From the Web, you may learn that in the year 2015 an average american household consumed \(10.8 \mathrm{kWh}\) per day, or \(901 \mathrm{kWh}\) per month. Simple? well, definitely simpler to comprehend than if the same Web source said: "3,243,600,000 Joules per month".