Please answer question 3.4-14:
3.4-11. Show that the pressure of a multicomponent simple ideal gas can be written as the sum of " partial pressures" P, where P, = N,RT/V. These "partial pressures" are purely formal quantities not subject to experimental observation. (From the mechanistic viewpoint of kinetic theory the partial pressure P, is the contribution to the total pressure that results from bombardment of the wall by are noninteracting, as in an ideal gas.) molecules of species i--a distinction that can be made only when the molecules multicomponent simple ideal gas, satisfies 3.4-12. Show that , the electrochemical potential of the jth component in a =RTln - (function of T) and find the explicit form of the "function of T." 3.4-11) and the temperature. 3.4-13. An impermeable, diathermal, and rigid partition divides a container into two subvolumes, each of volume V. The subvolumes contain, respectively, one
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Some Formal Relationships and Sample Systems
mole of H, and three moles of Ne. The system is maintained at constant temperature T. The partition is suddenly made permeable to H,, but not to Ne, and equilibrium is allowed to reestablish. Find the mole numbers and the pressures. 3.4-14. Use the results of Problems 3.4-11 and 3.4-12 to establish the results P. = P, and P = 2P. in the demonstration of Gibbs's theorem at the end of this section.
