Find the enthalpy and entropy of seawater at 40°C.
Solution
= 12.552 + 0.8368(313.15 - 288.15) = 33.472 kJ / kg
313.15
288.15
Mixing is an irreversible process; hence, the entropy of a mixture at a specified temperature and pressure is greater than the sum of the entropies of the individual components at the same temperature and pressure before mixing. Therefore, since the entropy of a mixture is the sum of the entropies of its components, the entropies of the components of a mixture are greater than the entropies of the pure components at the same temperature and pressure. The entropy of a component per unit mole in an ideal solution at specified pressure P and temperature T is given by (Cengel and Boles, 1998):
It should be noted that ln(xi) is a negative quantity, as xi < 1, and therefore —R ln(xi) is always positive. Equation (8.12) proves the statement made earlier that the entropy of a component in a mixture is always greater than the entropy of that component when it exists alone at a temperature and pressure equal to that of the mixture. Finally, the entropy of a saline solution is the sum of the entropies of salt and water in the saline solutions (Cerci, 2002):
= Xs [ Ss,pure(T,P) - R ^ )] + [ ,pure(T, P) - R ln()]
= XxSs,pure(T,P) - R[ x, ln(x,) + xw ln(xw)] (8.13)
The entropy of saline water per unit mass is determined by dividing the above quantity, which is per unit mole, by the molar mass of saline water. Therefore,
(T, P ) + mfwSw,pure(T, P) - R[x,ln(x,) + xwln(xw)] [kJ/kg- (8.14)
The exergy of a flow stream is given as (Cengel and Boles, 1998):
Finally, the rate of exergy flow associated with a fluid stream is given by
Using the relations presented in this section, the specific exergy and exergy flow rates at various points of a reverse osmosis system can be evaluated. From the exergy flow rates, the exergy destroyed within any component of the system can be determined from exergy balance. It should be noted that the exergy of raw brackish or seawater is 0, since its state is taken to be the dead state. Also, exergies of brine streams are negative because they have salinities above the dead state level.
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