GENERAL GAS LAWWe have learned that Boyle’s law pertains tosituations in which the temperature remainsconstant (fig. 11-4), and that Charles’s lawpertains to situations in which pressure remainsconstant (fig. 11-4). It is usually not possible tocontrol pressure or temperature in tanks or bottlesof gas subject to the weather and shipboarddemands. Boyle’s and Charles’s laws are com-bined to form the general gas law. This law states:The product of the initial pressure, initial volume,and new temperature (absolute scale) of anenclosed gas is equal to the product of the newpressure, new volume, and initial temperature. Itis a mathematical statement which allows manygas problems to be solved by using the principlesof Boyle’s law and/or Charles’s law. The equationis expressed asor(P and T represent absolute pressure and absolutetemperature, respectively.)You can see by examining figure 11-4 that thethree equations are special cases of the generalequation. Thus, if the temperature remainsconstant, T1 equals T2 and both can be eliminatedfrom the general formula, which then reduces tothe form shown in part A. When the volumeremains constant, V1 equals V2, thereby reducingFigure 11-4.—The general gas law.the general equation to the form given in part B.Similarly, P1 is equated to P2 for constantpressure, and the equation then takes the formgiven in part C.The general gas law applies with exactness onlyto “ideal” gases in which the molecules areassumed to be perfectly elastic. However, itdescribes the behavior of actual gases withsufficient accuracy for most practical purposes.Two examples of the general equation follow:1. Two cubic feet of a gas at 75 psig and 80°Fare compressed to a volume of 1 cubic foot andthen heated to a temperature of 300°F. What isthe new gauge pressure?Using equation 11-9, P1V1T2 = P2V2T1, whereV1 is 2 ft3, P1 is 75 psig, T1 is 80°F, V2 is 1 ft3and T2 is 300°F:Solution:Substituting:Converting absolute pressure to gauge pressure:2. Four cubic feet of a gas at 75 psig and 80°Fare compressed to 237.8 psig and heated to atemperature of 300°F. What is the volume of thegas resulting from these changes? Using equation11-9, P1V1T2 = P2V2T1, where V1 is 4 ft3, P2 is11-6
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