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phys documents (dragged) 42 - α β and γ holds G α m = G...

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36 Physics Formulary by ir. J.C.A. Wevers 3. Isothermic compression at T 2 , removing Q 2 from the system. 4. Adiabatic compression to T 1 . The efFciency for Carnot’s process is: η =1 - | Q 2 | | Q 1 | =1 - T 2 T 1 := η C The Carnot efFciency η C is the maximal efFciency at which a heat machine can operate. If the process is applied in reverse order and the system performs a work - W the cold factor is given by: ξ = | Q 2 | W = | Q 2 | | Q 1 | - | Q 2 | = T 2 T 1 - T 2 The Stirling process Stirling’s cycle exists of 2 isothermics and 2 isochorics. The efFciency in the ideal case is the same as for Carnot’s cycle. 8.7 Maximal work Consider a system that changes from state 1 into state 2, with the temperature and pressure of the surroundings given by T 0 and p 0 . The maximum work which can be obtained from this change is, when all processes are reversible: 1. Closed system: W max =( U 1 - U 2 ) - T 0 ( S 1 - S 2 )+ p 0 ( V 1 - V 2 ) . 2. Open system: W max =( H 1 - H 2 ) - T 0 ( S 1 - S 2 ) - Δ E kin - Δ E pot . The minimal work needed to attain a certain state is: W min = - W max . 8.8 Phase transitions Phase transitions are isothermic and isobaric, so dG =0 . When the phases are indicated by
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Unformatted text preview: α , β and γ holds: G α m = G β m and Δ S m = S α m-S β m = r βα T where r βα is the transition heat of phase β to phase α and T is the transition temperature. The following holds: r βα = r αβ and r βα = r γα-r γβ . ±urther S m = ± ∂ G m ∂ T ² p so G has a twist in the transition point. In a two phase system Clapeyron’s equation is valid: dp dT = S α m-S β m V α m-V β m = r βα ( V α m-V β m ) T ±or an ideal gas one Fnds for the vapor line at some distance from the critical point: p = p e-r βα /RT There exist also phase transitions with r βα = 0 . ±or those there will occur only a discontinuity in the second derivates of G m . These second-order transitions appear at organization phenomena . A phase-change of the 3rd order, so with e.g. [ ∂ 3 G m / ∂ T 3 ] p non continuous arises e.g. when ferromagnetic iron changes to the paramagnetic state....
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