Energy is a fundamental concept and is central to many different scientific and engineering applications. As a result, energy can be reported in an incredibly large number of different units, many of which are common in particular fields but are almost unheard of in other areas. If you are shopping for a furnace to heat your house, you will likely compare your choices in terms of the heat they can deliver, measured in BTUs (British thermal units). If you are dieting and want to compare the energy content of two snacks, you might read the label for Calorie content (these are actually kilocalories - more on this below). And if you are a scientist, wanting to investigate changes in internal energy
U = q + w
you probably will want to work in Joules. Note that since q (heat) and w (work) are changes in internal energy, they will have energy units, too. The units you chose to employ should not, of course, change the absolute amount of energy involved and if you use the proper conversion factors, you should be able to compare energies given in dissimilar units.
For example, in S.I. units, energy is measured in Joules. Energy units are not fundamental; they can be expressed in other, simpler units. To see what these composite units are, let's calculate the kinetic energy (K.E.) of a 2.0 kilogram mass moving at 1.0 meters/second.
K.E. = (1/2) m v2 = (1/2)(2.0 kg)(1.0 m/s2) = 1.0 kg-m/s2
Energy, therefore, has units of kg-m/s2 and in S.I. units 1 Joule is defined to equal 1 kg-m/s2 exactly.
1 Joule = 1 kg-m/s2
Here's another problem that requires the measurement of energy. Let's say we want to heat up 1.0 gram of water by 1.0 oC. How much heat (q) would we need to supply? The specific heat of water is 1 calorie/g-oC (exact at 14.5 oC) and so
q = (1.0 g)(1.0 oC)(1 cal/g-oC) = 1.0 cal
Actually, the calorie is defined in just these terms. It is defined as the amount of heat needed to raise the temperature of water by one degree Celsius.If we were working in S.I. units and wanted to convert our value of heat in calories to heat in Joules we would simply employ the conversion factor so that units would cancel out to leave the desired ones.
Tables of conversion factors can generally be found in an appendix or within the front cover of physical chemistry texts. A few on-line sites are con1 and con2. There are also on-line converters that calculate the conversion for you. They simply act as a calculator doing the math shown above. Try calc1 or calc2 if you want to use one of these.
To get some feel for energy quantities it helps to see some average energy values. Dr. Giovanni Vidali, a Professor of Physics at Syracuse University, has tabulated an interesting set of data for this purpose. Look through the whole set; some of the most interesting comparisons are towards the end. To understand the ones involving power, remember that power is energy per unit time and that common power units are watts.
1 watt = 1 Joule/second
# Joules = # watts x # seconds
Finally, we promised to say something about the term "Calorie" that you find on food nutritional labels. One calorie (with a small c) is defined as the amount of heat needed to raise the temperature of 1 gram of water at 14.5 oC by one degree Celsius, and is equal to 4.184 Joules. One Calorie (with a capital C) is used to label the energy content of foods and is actually equal to one kilocaloire.
1 Calorie = 1000 calories = 1 kilocalories
1 Calorie = 4,184 Joules = 4.184 kJ
While the difference between labeling energy content in calories or in Calories (kilocalories) should be obvious from the capitalization of the c/C, sometimes people are pretty sloppy about it. You, therefore, have to be careful to evaluate your units in the context that they are reported. Food and exercise citations are almost always in Calories; other applications are probably calories.
