Power vs. Energy

I can get worked up about units, and this can really annoy people. It especially annoyed students I taught in grad school. I was pretty tyrannical when grading; they always had to include units in their calculations. They could have all the right numbers, but they didn’t get full credit unless all the units were right too. I have no regrets about being such a stickler, because I see tons of confusion about this in the building & energy fields. So here’s a rant about one of my pet peeves: power and energy.

Question: What’s the difference between Power and Energy?

Is this some kind of philosophical question? A koan to meditate upon? No. There’s a real answer (in the engineering world at least). Power is the rate of energy.

A few common units of energy:

  • British Thermal Unit (Btu)
  • Joule (J)
  • Watt-hour (Wh)

A few common units of power:

  • Watt (W)
  • Btu per hour (Btu/h)
  • horsepower (hp)

The relationship between Btu and Btu/h is pretty obvious: power (Btu/h) is energy (Btu) divided by time (hour). You’ll also see kBtu (1,000 Btu) and MMBtu (1,000,000 Btu), but be careful when you see MBtu (sometimes this means 1,000 Btu, sometimes 1,000,000 Btu – it comes from confusion of metric and IP prefixes).

Unfortunately, a lot of heating equipment cut sheets list capacities in “Btuh” but what they mean is “Btu/h.”  Maybe this goes back to the typesetting days and boiler manufacturers didn’t want to pay for the “/.”

Yes, sure, most people generally know that “Btuh” really is a thermal power measurement (heat energy delivered over time), but some people think the same thing applies to “Wh” and “kWh.” THIS IS NOT TRUE!  A kilowatt-hour is NOT a “kilowatt per hour.” A kWh is a kilowatt times an hour.

As an example, take a 100-Watt light bulb. First, you should be embarrassed for using an incandescent lamp. Throw it out and get a 10-Watt LED. Now let’s say you run this 10-Watt LED for five hours.

Question: How much power does it use over this time?

Answer: 10 Watts.

Okay, that was kind of a trick question. It’s only ever going to use 10 Watts (as long as it’s working normally). But that’s my point.

Question: How much energy does it use over this time?

Answer: 50 Watt-hours (10 W x 5 h = 50 Wh)

If you run this 5 hours/night for 30 nights it’ll consume 1,500 Wh or 1.5 kWh. And if this LED is in your house, at the end of the month you’ll likely get an electric bill based on how many kilowatt-hours (kWh) you used over the month. I think the average in the Northeast is about 600 kWh/month; you can check EIA for details.

It works the same for generation. If you have a 300-Watt solar electric module and it’s sitting at standard test conditions for 10 hours it will generate 3 kWh of energy. (Yes, yes, standard test conditions never really occur in the real world. And yes, there are lots of other system inefficiencies to think about. It’s just an example! Cut me some slack.)

So when I hear someone say, “I reduced my electric use by 200 kilowatts last month,” why do I flip out? Because that’s a fantastic improvement? Or because they should have saved more? No. It’s because what they mean is they saved “200 kilowatt-hours” last month.

“Isn’t that nit-picking?” you ask. “Shouldn’t you just settle down?”

NO! Because many, many people really don’t understand this distinction. I’ve seen too many people fumble through calculations confusing kW and kWh and come up with ridiculous, meaningless, or just plain wrong results. These people have included building managers, solar contractors, licensed engineers, managers of efficiency programs, etc. I think it’d be good if more people understood this.

Also, many electricity rate structures include charges for both energy and peak power (demand). In a commercial building, a customer might pay $0.12/kWh for total energy used during the month and an additional $20/kW for the highest period of power consumption during the month. When you have fees for both kWh and kW it’s more obvious (and important) to differentiate them.

So pay attention to units! If people stop messing this up I won’t have to rant about other pet peeves. Like “hot water heaters.” Absurd! People don’t have “hot water heaters” in their homes. They have water heaters. Duh.

 

By Robb Aldrich, Senior Mechanical Engineer

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