Thermodynamics

6 | ThermodynamicsFIGURE 1–6The SI unit prefixes are used in allbranches of engineering.200 mL(0.2 L)1 kg(10 3 g)1 M(10 6 )m = 1 kgm = 32.174 lbma = 1 m/s 2a = 1 ft/s 2F = 1 NFIGURE 1–7The definition of the force units.1 applem = 102 g1 N10 applesm = 1 kg1 kgfF = 1 lbf4 applesm = 1 lbm1 lbfFIGURE 1–8The relative magnitudes of the forceunits newton (N), kilogram-force(kgf), and pound-force (lbf).Some SI and English UnitsIn SI, the units of mass, length, and time are the kilogram (kg), meter (m),and second (s), respectively. The respective units in the English system arethe pound-mass (lbm), foot (ft), and second (s). The pound symbol lb isactually the abbreviation of libra, which was the ancient Roman unit ofweight. The English retained this symbol even after the end of the Romanoccupation of Britain in 410. The mass and length units in the two systemsare related to each other by1 lbm 0.45359 kg1 ft 0.3048 mIn the English system, force is usually considered to be one of the primarydimensions and is assigned a nonderived unit. This is a source of confusionand error that necessitates the use of a dimensional constant (g c ) inmany formulas. To avoid this nuisance, we consider force to be a secondarydimension whose unit is derived from Newton’s second law, that is,Force 1Mass2 1Acceleration2orF ma(1–1)In SI, the force unit is the newton (N), and it is defined as the force requiredto accelerate a mass of 1 kg at a rate of 1 m/s 2 . In the English system, theforce unit is the pound-force (lbf) and is defined as the force required toaccelerate a mass of 32.174 lbm (1 slug) at a rate of 1 ft/s 2 (Fig. 1–7). Thatis,1 N 1 kg # m>s21 lbf 32.174 lbm # ft>s2A force of 1 N is roughly equivalent to the weight of a small apple (m 102 g), whereas a force of 1 lbf is roughly equivalent to the weight of fourmedium apples (m total 454 g), as shown in Fig. 1–8. Another force unit incommon use in many European countries is the kilogram-force (kgf), whichis the weight of 1 kg mass at sea level (1 kgf 9.807 N).The term weight is often incorrectly used to express mass, particularly bythe “weight watchers.” Unlike mass, weight W is a force. It is the gravitationalforce applied to a body, and its magnitude is determined from Newton’ssecond law,W mg1N2(1–2)