"Power" is one of many terms used loosely in everyday discourse that has a very specific meaning in physics. Others include force, mass, energy, current – the list is all but endless.
In physics parlance, power is simply energy per unit time, or alternatively, work per unit time, since work and energy are expressed in the same units – usually joules (J), which is the SI, or standard international, unit, but also ergs or, in calculations where heat is under consideration, either calories or BTU. Energy, in turn, is the product of force and distance. Force, the SI unit for which is the newton, is the product of mass and acceleration.
All of this is simply background, though. At times, you'll need to express power in terms of heat by linking these different units through time, using either multiplication or division. Watts to BTU is an example of such a conversion.
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Force, as noted, is the product of mass and acceleration:
F = ma
Here, in the SI scheme, force has units of newtons, mass is expressed in kilograms and acceleration is measured in meters per second squared, or m/s2.
When a force acts on an object and causes it to move, the product of the applied force and the distance the object moves is the energy required to get the job done. The SI unit, the joule, can be expressed to simplify some calculations as a newton-meter.
Finally, energy output per unit time yields power. Again sticking to SI units, joules divided by seconds reduces to another SI unit, the watt. Thus 1 watt (W) is one joule of energy expended over the course of one second (1 J/s).
Energy and Power in the Everyday World
When you encounter a reference to the horsepower of, say, an automobile, you are seeing a formal declaration of the power of that machine's engine. 1 horsepower (hp) equals 745.7 watts. Since the horsepower of motor vehicles is usually in the hundreds, you can see that, for everyday purposes, a watt, and by extension a joule, is not a very large amount of power or energy respectively.
As an example, 1 joule is approximately the amount of energy required to raise a 100-gram (0.1-kg) object, such as an apple, 1 meter upward against the force of gravity acting in the opposite direction of the work performed.
The BTU, short for British Thermal Unit, is defined as the amount of heat (energy) required to raise the temperature of 1 pound of water by 1 degree Fahrenheit. This introduces a complication into most physics problems, where mass is measured in kilograms (or various powers of ten of kilograms) and degrees are measured in Celsius, also called centigrade. 1 BTU works out to 1055.056 joules, or equivalently, 1 BTU = 1055.056 watt-seconds.
At times, it is useful to calculate heat dissipation from power consumption in a home or office setting. Utility companies measure the amount of energy a facility uses, often per month, in kilowatt-hours, or kWh. Remembering that power is energy per unit time, it follows that energy is power multiplied by time. Utilities providers use kilowatts times hours rather than the SI unit of watts times seconds, or joules, to make the numbers more convenient to use.
The most fundamental conversion between a measurement involving watts, specifically kWh, and BTU is:
1 kWh = 3,412 BTU
Because the units of watts and BTU are different, you have to decide the time frame over which to relate these quantities. For more examples, see the linked RapidTables page (under Resources).