The - diagram of water is read as follows: triple point at and ; critical point at…

PHYSICS · Multi-part · Fermi University Physics · Thermal, Statistical & Complex Systems · Thermodynamic potentials and the formal structure of thermodynamics · Interacting systems, real gases and phase equilibria

Thermal Physics, Ch Phase coexistence and the Clausius-Clapeyron relation

Problem

The

p

T

diagram of water is read as follows: triple point at

273.16\,\mathrm{K}

and

612\,\mathrm{Pa}

; critical point at

647\,\mathrm{K}

and

22.1\,\mathrm{MPa}

; melting line straight with slope

\mathrm{d}p/\mathrm{d}T = -13.5\,\mathrm{MPa\,K^{-1}}

through the triple point; boiling line through

101.3\,\mathrm{kPa}

373.15\,\mathrm{K}

. The latent heat of fusion at

273.15\,\mathrm{K}

L_f = 6.01\,\mathrm{kJ\,mol^{-1}}

. A separate temperature-composition diagram at fixed pressure is given for a binary alloy of metals M and N, with

x

the mole fraction of N. At one temperature the tie line runs from

x_L = 0.18

in the liquid to

x_S = 0.48

in the solid. ((a)) A block of ice at

271.00\,\mathrm{K}

is compressed isothermally from atmospheric pressure. At what pressure does it meet a coexistence line, and what happens there? Take the melting line to keep its stated slope over this range. ((b)) Sketch the molar Gibbs functions

g_{\rm ice}(T)

and

g_{\rm water}(T)

against

T

at one atmosphere over the range

268\,\mathrm{K}

278\,\mathrm{K}

, mark the metastable continuation of each curve, and find the magnitude of the difference between the slopes

(\partial g/\partial T)_p

of the two curves where they cross. ((c)) A charge of

10.0\,\mathrm{mol}

of the alloy, of overall composition

x_0 = 0.30

, is held at the temperature of the given tie line. How many moles of it are solid?

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