Thermodynamics

Dalton’s and Amagat’s laws can be expressed as follows:kDalton’s law: P m a P i 1T m , V m 2 exact for ideal gases, (13–6)i1∂ approximatekfor real gasesAmagat’s law: V m a V i 1T m , P m 2(13–7)i1In these relations, P i is called the component pressure and V i is called thecomponent volume (Fig. 13–7). Note that V i is the volume a componentwould occupy if it existed alone at T m and P m , not the actual volume occupiedby the component in the mixture. (In a vessel that holds a gas mixture,each component fills the entire volume of the vessel. Therefore, thevolume of each component is equal to the volume of the vessel.) Also, theratio P i /P m is called the pressure fraction and the ratio V i /V m is calledthe volume fraction of component i.Chapter 13 | 685O 2 + N 2100 kPa400 K1 m 3 O 2100 kPa400 K0.3 m 3 N 2100 kPa400 K0.7 m 3FIGURE 13–7The volume a component wouldoccupy if it existed alone at themixture T and P is called thecomponent volume (for ideal gases, itis equal to the partial volume y i V m ).Ideal-Gas MixturesFor ideal gases, P i and V i can be related to y i by using the ideal-gas relationfor both the components and the gas mixture:Therefore,P i 1T m , V m 2P mV i 1T m , P m 2V m N iR u T m >V mN m R u T m >V m N iN m y i N iR u T m >P mN m R u T m >P m N iN m y iP iP m V iV m N iN m y i(13–8)Equation 13–8 is strictly valid for ideal-gas mixtures since it is derived byassuming ideal-gas behavior for the gas mixture and each of its components.The quantity y i P m is called the partial pressure (identical to the componentpressure for ideal gases), and the quantity y i V m is called the partial volume(identical to the component volume for ideal gases). Note that for an ideal-gasmixture, the mole fraction, the pressure fraction, and the volume fraction of acomponent are identical.The composition of an ideal-gas mixture (such as the exhaust gases leavinga combustion chamber) is frequently determined by a volumetric analysis(called the Orsat Analysis) and Eq. 13–8. A sample gas at a knownvolume, pressure, and temperature is passed into a vessel containingreagents that absorb one of the gases. The volume of the remaining gas isthen measured at the original pressure and temperature. The ratio of thereduction in volume to the original volume (volume fraction) represents themole fraction of that particular gas.Real-Gas MixturesDalton’s law of additive pressures and Amagat’s law of additive volumescan also be used for real gases, often with reasonable accuracy. This time,however, the component pressures or component volumes should be evaluatedfrom relations that take into account the deviation of each component