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Unformatted text preview: s Definition of ∆ S at a process of the free expansion of an ideal gas : Initial state i (Fig. 201a) → final state f (Fig. 201b) is an irreversible process; all the molecules of the gas will never return to the left half of the container. 1 Irreversible process Fig. 201 Free expansion s In an ideal gas, p and V are state properties , not depend on the process. Other state properties are T and E int ( 內能 ). s We now assume that the gas has still another state p V Fig. 202 2 property — its entropy S . Furthermore, we define the change in entropy ∆ S of a system during a process from an initial state i to a final state f Here Q is the energy transferred as heat to or from the system during the process, and T is the temperature of the system in kelvins. s There is a problem, however, in applying Eq. 201 to the free expansion of Fig. 201 . As the gas rushes to fill the entire container, “p, T, and V” of the gas fluctuate unpredictably ( 無法預知 ). → In other words, they do not have a sequence of well defined equilibrium values during the intermediate stage o the change from initia state to fina state f 3 stages of the change from initial state i to final state f . Thus, we cannot trace ( 描繪 ) a p–V path for the free expansion and, more important, we cannot find a relation between Q and T that allows us to integrate as Eq. 201 requires. s However, if S is truly a state property, ∆ S between states i and f must depend only on those states and not at all on the process. s Suppose that we replace the irreversible free expansion with a reversible process that connects same states i and f . With a reversible process we can trace a p–V path on a pV plot, and we can find a relation between Q and T that allows us to use Eq. 201 to obtain ∆ S. s We saw that T i =T f =T during a free expansion. Thus, point and mus be on the same isotherm 等溫線 4 points i and f must be on the same isotherm ( 等溫線 ). → A convenient replacement process is a reversible isothermal expansion from state i to state f , which actually proceeds along that isotherm. Irreversible process Fig. 201 The free expansion process can be replaced by the reversible isothermal expansion process: 5 Reversible process Fig. 203 Isothermal expansion p 28. p 13. Free expansion p 29. s The reversible isothermal expansion is physically quite different from the irreversible free expansion . However, both processes have the same initial state and the same final state and thus must have the same ∆ S . 6 → ∆ S isoth = ∆ S free exp Because we removed the lead shot slowly, the intermediate states of the gas are equilibrium states, so we can plot them on a pV diagram (Fig. 204)....
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This note was uploaded on 12/27/2011 for the course LSCI 103 taught by Professor K.y.liao during the Fall '11 term at National Cheng Kung University.
 Fall '11
 K.Y.Liao

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