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A family spent \$235.25 in the month of February to heat their house.

a) Calculate the kilowatts of energy they consumed given that the price of electricity is \$0.09/kWh (kilowatt hour). Assume there are 28 days in February.

I came up with 672 kW, but I think that's wrong because 672 kW $\times$ \$0.09/kWh doesn't add up to \$235.25.

I think the problem I'm having here is that I'm not understanding what a kWh is. I know that a kWh is 1$\,$kW $\times$ 1$\,$h, but I don't know what that means. I mean, kWh is not the same as 1 kilowatt per hour, so what does kW $\cdot$ h mean?

Also, I don't think I understand what this problem wants. Do they want the kilowatts the family used in 28 days?

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hmm, after 0.09 kw * h, it does a strange format automatically. – ShrimpCrackers Oct 30 '12 at 8:51
You aren't using the $ character correctly. Use one in front of the latex expression, and one after it. – Alex Oct 30 '12 at 8:55
How did you get 672? I suspect you weren't even using all the information available to you, since 672 happens to be the number of hours in February (no matter how much electricity you use and what it costs). – Henning Makholm Oct 30 '12 at 9:32
The question should read: "Calculate the average power consumption (in kW) in February". 1 kW is the same as 1.36 HP. – Christian Blatter Oct 30 '12 at 9:35
up vote 1 down vote accepted

A kilowatt is not an amount of energy, it is a a rate of energy use.

For example, a particular heater might be using 2 kilowatts when it is turned on -- whenever it is turned on and for all the time it is turned on. If you turn it on for 3 hours you have to pay the utility company for $2\cdot 3=6$ kilowatt-hours of electricity. Of if you turn it on for half an hour you will have used $1$ kilowatt-hour.

That sounds like a somewhat strange sort of units to use, but it is traditionally used in electricity billing because for technical reasons the rate at which energy is used at a particular moment (measured in (kilo)watts) is easier to define and measure than the total amount of energy used over a period (measured in kilowatt-hours).

Additionally, the capacity of electricity production and distribution systems is naturally measured in how much energy it can handle per unit time -- i.e. power, measured in kilowatts or megawatts. This also has to do with the fact that (in contrast to, say fuel oil) it is difficult and prohibitively expensive to store electric energy in large amounts, so in practice it has to be produced at the power plant at the same time you're using it, and at the same rate you're using it.

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You seem to take the Watt for a unit of energy, which it is not. Watts measure the rate of some energy conversion (something which is also called power). Energy is power $\times$ time, hence energy is measured in Watts $\times$ time, for example in kWh.

As a consequence, question a) Calculate the kilowatts of energy they consumed is nonsense.

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It might mean calculate their average energy consumption during all of Februrary. (Which would be abour 3.9 kW). – Henning Makholm Oct 30 '12 at 9:33

You would take 24 hrs x 28 days to equal the 672 hours per month. Take the 672 x .09 to equal $60.48. $235.25/60.48 to equal 3.88 3.89kw x 672 hrs is 2614.8 kWh x .09 per kWh is $235.26

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