Simple Nature - Light and Matter

f / A realistic drawing of Joule’s apparatus, based on the illustrationin his original paper. The paddlewheel is sealed inside the can in themiddle. Joule wound up the two 13-kg lead weights and dropped them1.6 meters, repeating this 20 times to produce a temperature changeof only about half a degree Fahrenheit in the water inside the sealedcan. He claimed in his paper to be able to measure temperatures to anaccuracy of 1/200 of a degree.What about the factor of 1/2 in front? It comes out to beexactly 1/2 by the design of the metric system. If we’d been usingthe old-fashioned British engineering system of units (which is nolonger used in the U.K.), the equation would have been K = (7.44×10 −2 Btu · s 2 /slug · ft 2 )mv 2 . The version of the metric system calledthe SI, 5 in which everything is based on units of kilograms, meters,and seconds, not only has the numerical constant equal to 1/2, butmakes it unitless as well. In other words, we can think of the jouleas simply an abbreviation, 1 J=1 kg·m 2 /s 2 . More familiar examplesof this type of abbreviation are 1 minute=60 s, and the metric unitof land area, 1 hectare=10000 m 2 .Ergs and joules example 2⊲ There used to be two commonly used systems of metric units,referred to as mks and cgs. The mks system, now called the SI,is based on the meter, the kilogram, and the second. The cgssystem, which is now obsolete, was based on the centimeter, thegram, and the second. In the cgs system, the unit of energy isnot the joule but the erg, 1 erg=1 g · cm 2 /s 2 . How many ergs arein one joule?⊲ The simplest approach is to treat the units as if they were alge-5 Système International78 Chapter 2 Conservation of Energy