Thermodynamics

Chapter 13 | 707(d ) The osmotic pressure in this case is¢P min r m R w T 0 ln 11>y w 2 11028 kg>m 3 210.4615 kPa # m 3 >kg # K21288.15 K2ln 11>0.98882 1540 kPawhich is equal to the minimum gauge pressure to which seawater must becompressed if the fresh water is to be discharged at the local atmosphericpressure. As an alternative to pressurizing, the minimum height above thefresh water level that the seawater must be raised to produce fresh water is(Fig. 13–24)¢z min w min,ing1.50 kJ>kgDiscussion The minimum separation works determined above also representthe maximum works that can be produced during the reverse process of mixing.Therefore, 7.98 kJ of work can be produced when 0.0348 kg of salt ismixed with 0.9652 kg of water reversibly to produce 1 kg of saline water,and 1.50 kJ of work can be produced as 1 kg of fresh water is mixed withseawater reversibly. Therefore, the power that can be generated as a riverwith a flow rate of 10 6 m 3 /s mixes reversibly with seawater through semipermeablemembranes is (Fig. 13–25)W # max,out rV # w max,out 11000 kg>m 3 2110 6 m 3 >s2 11.50 kJ>kg2a 1 MW10 3 kJ>s b 1.5 10 6 MW9.81 m>s a 1 kg # m>s22 1 Nba 1000 N # mb 153 m1 kJwhich shows the tremendous amount of power potential wasted as the riversdischarge into the seas.Salinewater∆zMembraneP 2P 1Purewater∆P P 2 P 1FIGURE 13–24The osmotic pressure and the osmoticrise of saline water.Fresh and saline watermixing irreversiblyFresh riverwaterSea water salinity 3.48%z 153 mFresh and saline water mixing reversiblythrough semi-permeable membranes, andproducing powerFIGURE 13–25Power can be produced by mixing solutions of different concentrations reversibly.