Question

only 6...7...and 8

The Gibbs function of a thermodynamic system is defined by G H- TS. If the system is consisting of two phases 1 and 2 of a single substance and maintained at a constant temperature and pressure, the equilibriunm condition for the coexistence of these two phases is that the specific Gibbs functions are equal Consider now a first-order phase change between the phase 1 and the phase 2. At the phase boundary, the equilibrium condition for the two phases for the state A at T and P is given by gi(T P) g2fTP) and for the neighboring state B at (T+dT) and ( P+dP) is given by gr(T+dT.P+4P) = g2(T+dT,P+dP) v,-()_.G-1 or 2) 1- Show that the specific volume of the phase i is given by v 2- Show that the specific entropy of the phase i is given by: s,( 3 Using the equilibrium condition for the coexistence of two phases at the phase boundary and Taylor's aP /T (i-1 or 2) ar)p , theorem show that: (S2-sjdT (V2-V1)dP latent heat L T(s2 s1) specific volume for the vapor is very much larger than the specific volume for the liquid. 4 Deduce the Clausius-Clapeyron equation for the slope of the phase boundary (dPldT) as a function of the 5- Application: Find the equation of the vaporization curve for a perfect gas (PV nRT) assuming that the Consider now a second-order phase change between the phase 1 and 2. At the phase boundary, we consider the change in either s or v in going from one phase to another two neighboring states A at (T,P) and B at (T+dI, P+dP) Recall that, in a second-order phase change, there is no 6- Using the fact that there is no change in entropy at the phase boundary and Taylor's theorem, show that 1 dT-Tvß1dPe cp2 dT-Tvß2dp. (c,-T T) , see useful relations for the definition of β) 7- Deduce the first Ehrenfest equation for the slope of the phase boundary (dPidT) for a second-order phase 8- Using the fact that there is no change in volume at the phase boundary and Taylor's theorem, show that change

Answer 1

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