Powerless

From time to time we see reference to levels of voltage or temperature as units of power. For example, a recent Reuters article stated that a new kind of solar cell generated 7.8 volts of electricity, about “half the power” needed for some unspecified device. Hmm. In electrical systems power is the product of volts and amperes, or watts. That a solar cell generates volts says nothing about its ability to do useful work.

Most of us are familiar with the watt-hour, which we buy by the thousands as kilowatt-hours from the local electric utility for about 15 cents each. To put that in perspective, the common 100-watt light bulb requires both 100 volts and one ampere for 10 hours to consume the power of one kilowatt-hour. Or, the solar power cell at 7.8 volts would need to also produce a bit more than 12.8 amperes for 10 hours to produce a kilowatt-hour.

A similar misunderstanding equates temperature with a quantity of heat, or, in our day, the British Thermal Unit. A BTU is the amount of heat required at any temperature to raise a pound (or pint) of water one degree Fahrenheit. To calculate the amount of heat needed for a 10-minute, 120F shower with the well water at 50F, we need to know only the rate of flow per minute. For example, a water-saving shower head provides perhaps 2.5 gallons per minute, or 200 pounds for the shower. To have a warm shower, we need to raise the temperature of the water from 50 to 120F, or by 70F per pound. At one BTU per pound per degree, we need 14,000 BTUs for that shower. Finally, because 3,412 BTU equal one kilowatt-hour, the math gives 4.1 kilowatt-hours consumed at 15 cents per kilowatt-hour for a cost of a bit more than 61 cents.

We also can estimate the cost of power for our shower in another energy, such as fuel oil, which contains about 140,000 BTUs per gallon, or 10 times the quantity of heat needed. Assuming a total combustion efficiency of 70% and a cost of $3.00 a gallon of oil, we find that our warm shower would then cost about 43 cents.

The Reuters article shows an astonishing low level of understanding about things of fundamental importance to the subject, to its readers, and, one would hope, to Reuters. We also admit to a smile when populist energy ideas are boosted by those who don’t know power.