The - diagram of nitrogen is specified by these readings: triple point at and ;…

PHYSICS · Multi-part · Fermi University Physics · Thermal, Statistical & Complex Systems · Interacting systems, real gases and phase equilibria · Interacting systems, real gases and phase equilibria

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

Problem

The

p

T

diagram of nitrogen is specified by these readings: triple point at

63.15\,\mathrm{K}

and

12.5\,\mathrm{kPa}

; critical point at

126.2\,\mathrm{K}

and

3.39\,\mathrm{MPa}

; the liquid-vapour line runs from the triple point up to the critical point and passes through

101.3\,\mathrm{kPa}

77.4\,\mathrm{K}

. The latent heat of vaporisation at

77.4\,\mathrm{K}

5.58\,\mathrm{kJ\,mol^{-1}}

. A temperature-composition diagram at fixed pressure is also given for a binary alloy of two metals, with

x

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

x_L = 0.10

in the liquid to

x_S = 0.35

in the solid. ((a)) Read off the highest pressure at which liquid nitrogen can coexist with its vapour, and the lowest. ((b)) On the

101.3\,\mathrm{kPa}

isobar the molar Gibbs functions of liquid and vapour cross at

77.4\,\mathrm{K}

. Using

(\partial g/\partial T)_p = -s

, find the magnitude of the difference between the slopes of the two curves there. ((c)) An alloy of overall composition

x_0 = 0.22

sits on the given tie line. Find the fraction of it that is solid.

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