Entropy change mixing ideal gases

Just because this is the simple mixture, the partial entropy s may be interpreted as specific entropy of pure (ideal) gas at a density equal to those in the mixture (see (4.426) and below), and the mixing entropy may be calculated as the sum of entropy changes at the expansion of pure (ideal) gases a (with masses Wa) from starting density (before mixing) to final density (as in the mixture). 

Also of importance is the effect of temperature on the gas solubility. From this information it is possible to determine the enthalpy and entropy change experienced by the gas when it changes from the ideal gas state (/z and ) to the mixed liquid state ( andT,). 

Figure 2.13 Mixing of ideal gas A with ideal gas B at constant temperature and constant total pressure. The entropy change AS is given by equation (2.78).

The entropy changes ASa and ASB can be calculated from equation (2.69), which applies to the isothermal reversible expansion of ideal gas, since AS is independent of the path and the same result is obtained for the expansion during the spontaneous mixing process as during the controlled reversible expansion. Equation (2.69) gives... 

In Appendix H, we have examined processes involving mixing and assimilation in ideal-gas systems. We have seen that mixing in itself does not contribute anything to the thermodynamics of the process, whereas assimilation and deassimilation do. We now examine similar processes in nonideal systems where intermolecular interactions exist. We shall examine the change in the Gibbs energy, rather than the entropy. But the conclusions are the same. 

Using the energy, volume, and entropy changes on mixing given here, one can easily compute the other thermodynamic properties of an ideal gas mixture (Problem 9.1). The results are given in Table 9.1-1. Of particular interest are the expressions for... 

Isothermal-isobaric mixing. Consider Nj moles of pure ideal gas 1 and N2 moles of pure ideal gas 2 initially in separate containers at the same T and P. We mix these two gases in such a way that the mixture remains at the same T and P note this is the reverse of the process shown in Figure 4.1. We want to determine whether the change in entropy is positive, negative, or zero. The entropy change is given by... 

Ideal Gas Mixing. When C species are mixed at constant pressure and temperature, as illustrated in Figure 9.9. the change in the entropy flow rate is given by Eg. 19.10). applied separately for each species j ... 

Figure 3.9 pertained to 1.00 mole each of helium and neon. The exercise focused on the mixing of gases and maximization of entropy, (a) Show that the maximum total change in the entropy for the composite system is = 2 moles xRx log (2). (b) The chemical potential for an ideal gas includes a term that depends only on temperature. In arriving at, what is the fate of the °(r) terms ... 

When pure ideal gases mix at constant T and p to form an ideal gas mixture, the molar entropy change A5 (mix) = -R yt In (Eq. 11.1.9) is positive. 

Consider a pure ideal-gas phase. Entropy is an extensive property, so if we divide this phase into two subsystems with an internal partition, the total entropy remains unchanged. The reverse process, the removal of the partition, must also have zero entropy change. Despite the fact that the latter process allows the molecules in the two subsystems to intermingle without a change in T or />, it cannot be considered mixing because the entropy does not increase. The essential point is that the same substance is present in both of the subsystems, so there is no macroscopic change of state when the partition is removed. 

So, for both the spontaneous expansion of an ideal gas and the spontaneous mixing of ideal gases, there is no change in internal energy (or enthalpy) but an increase in entropy It seems possible that increases in entropy underlie spontaneous processes. We will soon see that the characteristic feature of a spontaneous process is that it causes the entropy of the universe to increase. 

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