706 | Thermodynamics
water from the sea, and (d) the minimum gauge pressure that the seawater
must be raised if fresh water is to be obtained by reverse osmosis using
semipermeable membranes.Solution Fresh water is to be obtained from seawater. The mole fractions of
seawater, the minimum works of separation needed for two limiting cases,
and the required pressurization of seawater for reverse osmosis are to be
determined.
Assumptions 1 The seawater is an ideal solution since it is dilute. 2 The
total dissolved solids in water can be treated as table salt (NaCl). 3 The envi-
ronment temperature is also 15°C.
Properties The molar masses of water and salt are Mw 18.0 kg/kmol
andMs58.44 kg/kmol. The gas constant of pure water is Rw0.4615
kJ/kg · K (Table A–1). The density of seawater is 1028 kg/m^3.
Analysis (a) Noting that the mass fractions of salts and water in seawater
are mfs0.0348 and mfw 1 mfs0.9652, the mole fractions are
determined from Eqs. 13–4 and 13–5 to be(b) The minimum work input required to separate 1 kg of seawater com-
pletely into pure water and pure salts isTherefore, it takes a minimum of 7.98 kJ of work input to separate 1 kg of
seawater into 0.0348 kg of salt and 0.9652 kg (nearly 1 kg) of fresh water.(c) The minimum work input required to produce 1 kg of fresh water from
seawater isNote that it takes about 5 times more work to separate 1 kg of seawater
completely into fresh water and salt than it does to produce 1 kg of fresh
water from a large amount of seawater.1.50 kJ/kg fresh water1 0.4615 kJ>kg#K 21 288.15 K 2 ln 11 >0.9888 2
wmin,inRwT 0 ln 11 >yw 2wmin,inwmin,in
Mm147.2 kJ>kmol
18.44 kg>kmol7.98 kJ/kg seawater147.2 kJ>kmol1 8.314 kJ>kmol#K 21 288.15 K 21 0.9888 ln 0.98880.0112 ln 0.0112 2
wmin,inRuT 01 yA ln yAyB ln yB 2 RuT 0 1 yw ln ywys ln ys 2ys 1 yw 1 0.98880.01121.12%ywmfwMm
Mw0.965218.44 kg>kmol
18.0 kg>kmol0.9888Mm1amfi
Mi1
mfs
Msmfw
Mw1
0.0348
58.440.9652
18.018.44 kg>kmol