Irreversible adiabatic expansion

For an irreversible adiabatic expansion in which some work is performed, the work performed is less in magnitude than that in the reversible process because the external pressure is less than the pressure of the gas by a finite amount. Thus, if the final volume V2 is the same as that in the reversible process, T2 will not be as low in... 

For an irreversible adiabatic expansion in which some work is performed, the work performed is less in magnimde than that in the reversible process because the external pressure is less than the pressure of the gas by a finite amount. Thus, if the final volume is the same as in the reversible process, the final temperature will not be as low in the irreversible process, because, according to Equation (5.47), the temperature drop depends directly on the work performed by the expanding gas. Similarly, from Equations (5.42) and (5.44), AC7 and A//, respectively, also must be numerically smaller in the intermediate expansion than in the reversible expansion. In the adiabatic expansion, from a common set of initial conditions to the same final volume, the values of Af7 and A//, as well as the values of the work performed, seem to depend on the path (see summary in Table 5.2). At first glance, such behavior seems to contradict the assumption that U and H are state functions. Careful consideration shows that the difference occurs because the endpoints of the three paths are different. Even though the final volume can be made the same, the final temperature depends on whether the expansion is free, reversible, or intermediate (Table 5.2). 

Points a and b in Figure 6.7 represent the initial and final states of an irreversible adiabatic expansion of an ideal gas. The path between is not represented because the temperature has no well-defined value in such a change different parts of the system may have different temperatures. The inhomogeneities in the system that develop during the irreversible change do not disappear until a new equilibrium is reached at b. 

A reversible adiabatic expansion of an ideal gas has a zero entropy change, and an irreversible adiabatic expansion of the same gas from the same initial state to the same final volume has a positive entropy change. This statement may seem to be inconsistent with the statement that 5 is a thermodynamic property. The resolution of the discrepancy is that the two changes do not constitute the same change of state the final temperature of the reversible adiabatic expansion is lower than the final temperature of the irreversible adiabatic expansion (as in path 2 in Fig. 6.7). 

Consider now adiabatic processes wherein no heat transfer occurs. We represent on the PV diagram of Fig. 5.6 an irreversible, adiabatic expansion of a fluid from an initial equilibrium state at point A to a final equilibrium state at point B. Now suppose the fluid is restored to its initial state by a reversible process. If the initial process results in an entropy change of the fluid, then there must be heat transfer during the reversible restoration process such that... 

For an irreversible adiabatic expansion of 5.00 mol of neon from an initial temperature of500.0 K and an initial volume of 50.00 L to a final volume of 100.00 L, find the final temperature, AU, and w if / (transferred) = 1.000 atm. Compare with the values for a reversible expansion from the same initial state to the same final volume. 

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