Example of Boyle’s law: 4 cubic feet ofnitrogen are under a pressure of 100 psi (gauge).The nitrogen is allowed to expand to a volumeof 6 cubic feet. What is the new gauge pressure?Remember to convert gauge pressure to absolutepressure by adding 14.7.Using equation 11-6, V1P1 = V2P2, where V1 is4 ft3, V2 is 6 ft, and P1 is 100 psig:CHARLES’S LAWBoyle’s law assumes conditions of constanttemperature. In actual situations this is rarely thecase. Temperature changes continually and affectsthe volume of a given mass of gas.Jacques Charles, a French physicist, providedmuch of the foundation for the modern kinetictheory of gases. Through experiments, he foundthat all gases expand and contract proportionallyto the change in the absolute temperature,providing the pressure remains constant. Therelationship between volume and temperature isknown as Charles’s law. It states: The volume ofa gas is proportional to its absolute temperature,if constant pressure is maintained. In equationform, this relationship may be expressed asEquation 11-7where V1 and V2 are the original and finalvolumes, and T1 and T2 are the original and finalabsolute temperatures.Since an increase in the temperature of a gascauses it to expand if the pressure is kept constant,it is reasonable to expect that if a given sampleis heated within a closed container and its volumeremains constant, the pressure of the gas willincrease. Experiments have proven this to be true.In equation form, this becomesP1T2 = P2T1Equation 11-8orThis equation states that for a constant volume,the absolute pressure of a gas varies directly withthe absolute temperature.Example: A cylinder of gas under a pressureof 1800 psig at 70°F is left out in the sun in thetropics and heats up to a temperature of 130°F.What is the new pressure within the cylinder?(Remember that both pressure and temperaturemust be converted to absolute pressure andabsolute temperature.)Converting absolute pressure to gauge pressure:11-5
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