Two independent design questions

PHYSICS · Multi-part · Fermi University Physics · Thermal, Statistical & Complex Systems · Thermodynamic potentials and the formal structure of thermodynamics · Thermodynamic potentials and the formal structure of thermodynamics

Thermal Physics, Ch Chemical potential, open systems and chemical equilibrium

Problem

Two independent design questions, each answered with one result of this chapter. ((a)) A reverse-osmosis plant treats brackish estuary water at

291\,\mathrm{K}

containing dissolved salts that supply a total of

0.72\,\mathrm{mol\,L^{-1}}

of dissolved ions. The membrane passes water only, the solution is treated as a dilute ideal solution, and the fresh-water side is at atmospheric pressure. By how much (in bar) must the pressure on the brackish side exceed that on the fresh side before any water at all is driven across? ((b)) An aircraft's barometer reads

0.55

of the sea-level pressure. Model the atmosphere as isothermal at

T = 255\,\mathrm{K}

, of uniform composition with mean molar mass

29.0\,\mathrm{g\,mol^{-1}}

, behaving as an ideal gas in a uniform field with

g = 9.81\,\mathrm{m\,s^{-2}}

. What height above sea level does that reading correspond to?

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