Nomenclature A = constant in nuclei above nuclei growth expression (eq 41, m/sec B = constant in nuclei above nuclei growth expression (eq 4) c = bulk solution concentration, kg/kg of solution c L = concentration a t crystal/solution interface, kg/kg of solution c * = saturation concentration, kg/kg of solution A c = overall concentration driving force (= c - c * for growth, = c * - c for dissolution), kg/kg of solution C = constant in BCF growth expression (eq 3), m/sec k = gas constant per molecule, J / K k d = rate constant for bulk diffusion step in crystal growth, kg/m2 sec k r = rate constant for surface integration step in crystal growth (eq 2), kg/m2 sec (kg/kg)' k,' = rate constant for surface integration step in crystal growth (eq 7), kg/m2 sec KD = overall mass transfer coefficient for dissolution process, kg/m2 sec K K = overall rate constant for crystal growth, kg/m2 sec (kg/kgI2 RD = dissolution rate, kg/m2 sec & = crystal growth rate, kg/m2 sec T = absolute temperature, K u = solution velocity (eq 9), cm/sec u = linear face growth rate, m/sec z = exponentineq2 Greek Letters y ' = edge free energy per growth unit, J q r = surface integration effectivness factor p = bulk solution concentration, kg/m3 of solution pi = concentration a t crystal/solution interface, kg/m3 of solution p* = saturation concentration, kg/m3 of solution u = supersaturation ( = ( p - p * ) / p * )
ui = supersaturation a t crystal/solution interface uc = constant in BCF growth expression (eq 3) Aw = overall concentration driving force, g/100 g of water Note
4.18 kJ/mol = 1kcal/mol
Literature Cited Bennema. P., J. Cryst. Growth, 5, 29 (1969). Bennerna. P., Boon, J., van Leeuwen, C., paper presented at 4th CHISA Congress, Prague, Sept 1972. Bennett, J. A. R . . Lewis, J. B.,A.I.Ch.E. J . , 4, 418 (1958). Bovington, C. H., Jones, A. L., Trans. Faraday Soc., 66, 2088 (1970). Brice, J. C., J. Cryst. Growth, 1, 161 (1967). Bujac. P. B. D . , Ph.D. Thesis, University of London, 1969. Burton, W. K.,Cabrera. N.. Frank, F. C.. Phil. Trans., A243, 299 (1951). Clontz, N. A., Johnson, R. T., McCabe, W. L.. Rousseau, R. W., Ind. Eng. Chem.. Fundam., 11, 368 (1972). Davey, R. J. and Mullin, J. W.. J . Cryst. Growth, in press, 1974. Garside. J,, Chem. Eng. Sci., 26, 1425 (1971 ) , Garside. J.. Mullin, J. W., Trans. lnst. Chem. Eng., 46, 11 (1968). Garside, J.. Mullin J. W.. Das, S. N., Ind. Eng. Chem.. Process Des. Develop., 12, 369 (1973). Gilmer, G. H., Bennema, P., J. Cryst. Growth, 13/14, 148 (1972). Jones, A . G., Mullin, J. W., Trans. Inst. Chem. Eng., 51, 302 (1973). Levins. D . M., Glastonbury, J. R., Trans. Inst. Chem. Eng., 50, 32, 132 (1972). Mullin, J. W., Garside. J.. Gaska. C., Chem. Ind., 1704 (1966). Mullin, J. W., Garside. J., Trans. lnst. Chem. Eng., 45, 291 (1967). Mullin, J. W., Gaska, C.. Can. J. Chem. Eng., 47, 483 (1969) Mullin, J. W., Gaska, C.. J. Chem. Eng. Data. 18, 217 (1973). Mullin, J. W., Nienow, A. W., J. Chem. Eng. Data. 9, 526 (1964). Nienow, A. W., Can. J. Chem. Eng., 47, 248 (1969). Rosen, H. N., Hulburt. A. M., Chem. Eng. Progr. Symp. Ser. No. 710. 67, 27 (1971). Rowe, P. N., Claxton, K. T . , Trans. lnst. Chem. Eng. 43, 321 (1965) Rumford, F.. Bain, J., Trans. Inst. Chem. Eng., 38, 10 (1960). Rushton. J. H.. Costick, E. W., Everett, H. J.. Chem. Eng. Progr., 46, 395, 467 (1950). Smythe. B. M . , Aust. J. Chem., 20, 1087 (1967). Zweitering. T. N.. Chem. Eng. Sci., 8,244 (1958)
Receiced for reuzex December 13,1973 Accepted June 17,1974 The authors are indebted to the Science Research Council for support of this work.
General Principles Underlying Chemical Cycles Which Thermally Decompose Water into the Elements Bernard M. Abraham* and Felix Schreiner Chemistry Division, Argonne National Laboratory. Argonne, Illinois 60439
The amount of heat required for the thermochemical decomposition of water by a multi-step reaction cycle operating between a high temperature TH and a low temperature TC is Q 2 - A G f o (H2O) ( T H / ( T H - T c ) ) . The thermal efficiency of decomposition cycles i s characterized by the figure of merit 7 = ( - A G f " ( H 2 0 ) / Q ) . This number decreases with increasing number of reaction steps if the additional steps are operated at intermediate temperatures. For heat economy inclusion of heat-absorbing steps below TH is preferable to the inclusion of heat-rejecting steps above Tc. The minimum number of reaction steps for thermochemical cycles operating between TH = 1000 K and Tc = 298.15 K is three as inferred from the required entropy change. The analysis of hypothetical and proposed real cycles by means of entropy vs. temperature diagrams is presented as a convenient method for the evaluation of water decomposition schemes.
Introduction After the pioneering work of Funk and Reinstrom (1966), interest in thermochemical cycles for splitting water developed rather slowly. As long as there appeared to be ample supplies of petrochemicals there was no eco-
nomic advantage to be gained by converting methane or naphtha into hydrogen which would then become a secondary fuel. Now, with the worldwide acceptance that there is a limit to the amount of petrochemicals which can be easily extracted from the earth, and with the recognition of the economies to be gained by piping gas rather than Ind. Eng. Chem., Fundam..Vol. 13, No. 4 , 1974
305
transmitting electricity, there is a kindling of interest in thermochemical cycles for splitting water with nuclear heat. The arguments in support of such programs are sufficiently compelling to give rise to a vigorous effort sponsored first by the Euratom combine (Euratom Joint Nuclear Research Center, Progress Report (1973), Bowman, et al. (1973), and later by others (Abraham, 1973a,b; de Beni, 1972; Hanneman, 1973). The "hydrogen economy" (de Beni 1970; "Chemical and Engineering News," staff reports, 1972a,b; Gregory, 1971; Gregory, 1973; Maugh, 1972, Winsche, 1973) has become a subject of widespread interest, and the rate a t which effort in developing thermochemical cycles is growing leaves little doubt that a consensus exists to the effect that the inexpensive production of large volumes of hydrogen is a desideratum. A thermochemical water splitting cycle is a regenerative sequence of chemical reactions which, by heat alone, decomposes water into hydrogen and oxygen. To decompose water alone by heat requires a temperature in excess of 3000 K, whereas heat sources in excess of 1100 K are not available. If water is to be decomposed a t ambient temperature (298.15 K) then an amount of electrical work equal to or greater than the negative of the Gibbs energy of formation must be supplied (237.2 kJ/mol). It is assumed here and throughout that all processes are conducted a t constant pressure equal to 1 atm. It is the goal of a thermochemical process to split the water into hydrogen and oxygen with essentially zero work entering into the reaction steps. Funk and Reinstrom (1966, 1972) have discussed the thermodynamics of multistep sequences. They did not, however, extend their analysis to establish the minimum number of reaction steps. Instead, they searched for a two-step sequence which, as will be shown in the next section, cannot satisfy the thermodynamic constraints. The chemical reactions entering into a sequence can be classified according to three essential functions: (1) water binding, (2) product recovery, and (3) reagent regeneration. A single reaction step can perform a dual function as is the case for the reverse Deacon reaction H,O(g)
+
C1, = 2HC1 + 1/20,
in which the water binding reaction is combined with the oxygen recovery. It is not possible, therefore, to state a priori the least number of steps required by a chemical cycle. We shall redevelop the thermodynamic equations which describe a thermochemical water splitting cycle and will show that implicit in the analysis is the minimum number of steps required for specified top and bottom temperatures.
Thermodynamic Principles All engines which employ heat to produce useful work are limited in efficiency by the second law of thermodynamics. This implies that once the highest operating temperature TH and the lowest operating temperature TC are known the maximum efficiency of the engine or process is also known. A thermochemical cycle which decomposes water into hydrogen and oxygen can be regarded as a thermal engine which produces work in the form of chemical potential energy. The theoretical efficiency arising from the second-law limitation as well as the energy balance which must satisfy the first law can be derived by reference to Figure 1. The figure illustrates a reversible engine, which in three different modes of operation, generates an amount of useful work W = - h G f " (HzO) where A G f o (H20) is the standard Gibbs energy of formation of liquid water a t Tc. 306
Ind. Eng. Chem., Fundam., Vol. 13, No. 4, 1974
CELL
4
w = ox
-= TH
- A G in20i ~
Figure 1. Schematic diagram of a sequence of reversible steps by which water can be decomposed into hydrogen and oxygen by absorbing heat from a reservoir a t T H .The three units enclosed by the dashed line, Carnot engine, electric generator, and electrolyzer are equivalent to a thermochemical water splitting cycle. Recombination of the gases in the fuel cell offsets the material change and the only effect that remains is the transfer of heat from TH to Tc and transformation of part of the heat into electrical energy.
In the first mode as a mechanical engine, an amount of heat Q is extracted from a reservoir a t TH and an amount q = Q x T c / T Hrejected to the low-temperature reservoir a t Tc. In the process the mechanical work W = Q - q is performed. In the second mode the work is used to generate an equivalent amount of electricity which is used to electrolyze water. A t the same time the amount of heat absorbed by the electrolysis cell is -TchSf" (HzO), where PSt" (H20) is the standard entropy of formation of liquid water a t Tc. Finally, in the third mode the work is recovered as electricity by recombining the hydrogen and oxygen in the fuel cell, and an amount of heat equal to -TASfo (Hz0) is transferred to the reservoir a t Tc. The "black box," outlined by the dotted lines, representing the Carnot engine, the generator, and the electrolyzer can be replaced by an equivalent "black box" representing a thermochemical cycle or chemical engine. Since the two black boxes are thermodynamically equivalent, no process which employs heat alone to decompose water can be more efficient than that illustrated by Figure 1. Therefore, the amount of heat which a process must absorb to decompose one mole of water is
Equation 1 is valid for any thermal process with top temperature TH and bottom temperature Tc. The chemical engine together with the fuel cell are completely cyclic in operation, as the only change is the conversion of heat into work; consequently, the sum of the positive entropy changes plus the sum of the negative entropy changes will equal zero. The minimum positive entropy change is readily deduced from eq 1, namely
Equation 2 specifies the minimum entropy change which
can introduce the requisite amount of heat into the system. The discussion so far has established a minimum heat absorption and a minimum entropy change which will produce one mole of hydrogen from water. It is also possible from eq 2 to establish the minimum number of steps or reactions. If one substitutes for -PGr" (HzO), TH, and Tc the numerical values 237.2 kJ, 1000 K, and 298.15 K, respectively, then it is found that
which is more than twice the entropy change for the decomposition of water into the elements. Clearly, a simple two-step process consisting of one heat absorbing and one heat rejection step is out of the question; the positive entropy change is too large for real substances. Large entropy changes can be obtained only by involving a large number of bonds either through several reaction steps or with several molecules in a single reaction. If the necessary additional steps can be added to absorb the heat, then there must also be steps to reject the heat a t lower temperatures, since the entropy changes must sum to zero. In general, then, steps will be added pairwise so the minimum number of reactions one might expect for a top temperature of 1000 K would be four. Included in the four is the recombination step so that the chemical engine alone will require three reactions, two heat absorbing steps and one heat rejection step. As the top temperature is reduced the number of reactions will perforce increase. We shall now show that a multistep cycle can indeed satisfy both the first and second laws along with the constraint that no useful work be expended in the process. Let it be assumed that a thermochemical cycle consists of j reactions, of which p have positive entropy changes and n have negative entropy changes. For simplicity and without loss of generality it shall be assumed that the sum of the heat capacities of the reactants is equal to the sum of the products. A phase change is considered a reaction step, as heat is absorbed or rejected isothermally; therefore, it must be included in the formalism. The stipulation that no useful work be done (Le., no work except expansion against the atmosphere) is equivalent to conducting each reaction a t equilibrium. For the ith reaction in the sequence
iTi
ASi d T =
C
AH, - TiASi
(4)
where AG," is the standard Gibbs energy change for the ith reaction a t the reference temperature Tc = 298.15 K. The j reactions in the sequence may now be summed to yield i
i
i
Since the enthalpy is a state function, the following equation holds for the sum of the enthalpy changes a t 298.15 K j
AHi
E
- AH,"(H,O)
= 285.8 kJ/mol
(6)
i=l
Therefore, from eq 5 and 6 we obtain j
f
C A H i = C T i A S i = - AHfo(H20) = i=l
P
TiASi = TIHASIH +
Q = i=l
T ~ H A S ~+H
(31
AS, = 0.3378 W/K
0 = - Wi = A G i = AG," -
place a t equilibrium. These sums, it must be recalled, include only the reactions in the chemical engine; they do not include the recombination of hydrogen and oxygen in the fuel cell. The total heat absorbed by the engine is obtained by summing the positive terms only
i=l
285.8 W/mol
(7)
for any chemical engine in which all the reactions take
.
-!-
TbHAS,,
(8)
and the heat rejected by summing the negative terms
c TiASi n
4 - 298.15 x ASf0(H20) =
i.1
TicASlc
+
TzcAS2c
+
...
=
+ TncAS,
(9)
Since the entropy is also a state function an equation similar to eq 6 is valid, namely
The heat absorbed and rejected during the heating and cooling of reactants and products is assumed to be equal so that the reactants are heated to the reaction temperature through perfect heat interchange with the products. The assumption that reactants and products have equal heat capacities is valid within about 5%; the assumption of perfect heat interchange belongs to a discussion of practical processes which is not being treated in this paper. A figure of merit q will now be defined by eq 11 as an aid in assessing the effect of increasing the number of steps in a cycle.
The standard Gibbs energy for water is used as the reference because water is fed in a t 298.15 K and the products are brought to 298.15 K. It is easy to see from eq 1 that for a process with one heat-absorbing step and one heat-rejecting step, which we shall call H C ( + l , -1) 77=
TH - Tc TH
or 7 equals the ideal Carnot efficiency. However, as was pointed out earlier, a real system cannot be found with only one heat-absorbing step. For heuristic purposes let it be assumed that reactions can be found with the required entropy changes a t arbitrary temperatures. It is now instructive to consider three hypothetical chemical engines with T1H = 1000 K and TIc = 298.15 K. One of these, HC(+2, - l j , will bind water as a liquid and will comprise two heat absorbing steps ( + 2 ) and one heat rejection step ( - l ) , a second HC(+2, -2) will bind water as a liquid and have an additional heat rejection step, and the third HC(+3, -2) will bind water as a gas so the additional heat absorbing step is the vaporization of water. In order to evaluate Q and ? each of these cycles assumptions must be made to reduce the number of variables. We make the plausible assumption that heat is absorbed or rejected in steps 2H and 2C with an entropy change of *0.150 k J / K . In HC(+3, -2), ASzH = 0.1090 kJ/mol, the entropy of vaporization of water a t 373.15 K. With these assumptions eq 7 and 10 can be solved simultaneously for A S ~ Hand ASIC, and then Q can be evaluated from eq 8 and used in the equation for u. The quantities calculated are tabulated in Table I where parentheses surround the postulated values. The table shows Ind. Eng. Chem., Fundarn., Vol. 13, No. 4 , 1974
307
Table I. Entropy Changes, Heat Absorbed, and Figure of Merit for Hypothetical Cycles ~~
Cycle HC(+1, HC(t2, HC(+2. HC(+3,
-1) -1)
-2) -2)
ASIC, kJ/K
ASzc, kJ/K
at 298.15 K
at 500 K
-0.1746 -0.2174 -0.1106 -0.2080
-
(-0.1500) (-0.1500)
ASlH, kJ/K a t 1000 K
ASzH, kJ/K a t 800 K
A S ~ HkJ/K ,
a t 373.15K
Q, k J
17
+0.3378 +0.2306 +0.2738 +0.2621
-
-
(+O. 1500) (+Os1500) (+O.1500)
-
337.8 350.6 393.8 422.8
0.702 0.676 0.602 0.561
-
0.1090
made to approach arbitrarily close to the ideal efficiency; the latter cannot.
J
500
1000 500 TEMPERATURE, KELVIN
1
1
I000
Figure 2. Entropy-temperature diagrams for four hypothetical thermochemical cycles operating between 298.15 and 1000 K . (The entropy changes a t 298.15 K include the entropy of formation of water.)
very clearly that the figure of merit decreases as reaction steps are added, although heat-absorbing steps below T H are not as deleterious as heat rejection steps above Tc. The information contained in Table I can also be displayed graphically. Knoche and Schybert (1972) displayed the Euratom Mark I cycle (Bowman, 1973; Euratom Joint Nuclear Research Center, Progress Report, 1973) and a cycle based on the hydrolysis of iron chloride with Mollier diagrams. These are rather awkward for chemical cycles which involve several temperatures because the temperature, a process variable, is the slope aH/aS = T in the Mollier diagram. The entropy-temperature diagram, on the other hand, is easily interpreted. The reaction steps are isothermals, the enclosed area is the work in this case equal to - A G f " (HzO), and the standard entropy change for the reaction may be plotted a t the reaction temperature since the entropy change is a slowly varying function of the temperature. The curves connecting the isothermals represent the entropy change for all material heated and cooled between isothermals; their slope is given azslaT = [ Z C , ] / T # 0. The curvature is small enough so they may be drawn as straight lines, although they will not, in general, be parallel. Entropy-temperature diagrams for the hypothetical cycles listed in Table I are displayed in Figure 2. The entropy of formation of liquid water A&" (HzO) = -0.1632 kJ/K has been included in the A S plotted a t 298.15 K; otherwise the diagram could not be closed. One sees that as the representation departs from a parallelogram the figure of merit diminishes. Since the enclosed area is a constant equal to 237.2 kJ, any indentation in the figure results, for constant TH - Tc, in a concomitant elongation of the isothermals, thereby increasing the amount of heat absorbed in the process. The diagrams point out a very essential distinction between a mechanical engine and a chemical one. The former can, in principle, be 308
Ind. Eng. Chern., Fundam., Vol. 13, No. 4, 1974
Thermodynamics of FeC12-Fe304 Sequences Cycles based on the hydrolysis of iron chloride have been presented in several variations (Euratom Joint Nuclear Research Center, Progress Report, 1973; Hanneman, 1973; Knoche, 1972). These are attractive because the maximum temperature 1100 K can be attained with a high-temperature gas-cooled reactor and the product gases occur in combinations which are easily separable. Fortunately, there are sufficient thermodynamic data available on the compounds entering into the reactions of each variation that sensible calculations can be made. It is useful to present the details of each cycle in diagrammatic form to assess the effect of slight differences. The data are taken from standard compilations of thermodynamic quantities (Rossini, 1952; Wagman, 1968) except for the enthalpy of fusion of FeC13, which was estimated. We shall compare the Mark 9 cycle proposed by C. Hardy (1973), the Agnes cycle of Hanneman and Wentorf (1973), and our own variation C(+5, -1). Mark 9 3FeC12(c) + 4H20(g) = Fe,O, + 6HCI
Fe,04
+
H2 (1108 K)
(1H)
3FeC1,(1) = 3FeC12(c) + 3/2C12 (775 K)
(2H)
3FeC13(c) = 3FeC1,(1) (555 K) = 3FeCI,(c) + 3H,O(g)
+ 6HC1 + 3/cIz
'hO2
(3H)
+
(497 K)
(IC)
The temperature after each reaction is the estimated temperature for .IG = 0 and was obtained by dividing the standard enthalpy change by the standard entropy change. The first three have positive entropy changes and the last one a negative entropy change. Agnes 3FeC12(c) + 4H@(g) = Fe304 + 6HC1
+ Hz (1108 K) MgC12 + H,O(g) = MgO + 2HC1 (795 K) 2FeC1,(1) = 2FeC1, + Clz (775 K)
(1H)
2FeCl,(c) = 2FeC1,(1) (555 K)
(4H)
MgO Fe,O,
+ Clz
= MgC12
+
3FeC1,
+
2FeC1,
'hO2 (692 K)
(3H) (2C)
+ 4HzO(g)
(519 K) (1C) Reactions 2C and 2H differ from those given by Hanneman and Wentorf by replacing Mg(OH)2 with MgO. This was done because the reactions as written by Hanneman and Wentorf would not go. C(+5, -1) +
8HC1 = FeClz
+
(2H)
4H,O(g) = Fe304 + 6HC1 + H,
Clz + HzO(g) = 2HC1
+
(1108 K) (1H)
'/202 (890 K)
(2H)
Table 11. Entropy Changes, Heat Absorbed, and Figure of Merit for Iron Chloride Cycles ASic, kJ/K
Cycle
AS,,. kJ/K
ASIH, kJ/K
A S z H ,kJ/K
ASsH, kJ/K
ASaH, kJ/K
Q, kJ
17
-
+0.2893
+O. 1266
+O. 1350
-
-0.0578
+0.2893
+o. 1222
+0.0844
+0.090
+0.2893
+0.0642
+ 0.0842
+0.090
537.5 (496.8) 577.0 (536.3) 537.0 (496.3)
0.441 (0.477) 0.411 (0.442) 0.442 (0.478)
0.5065
Mark 9
-
Agnes
-0.4837
C(+5, -1)
-
0.4837
-
I
I
t
i
AGNES
;:'$)
~~
-
-
-
-
1
1
1
1
'
TEMPERATURE, KELVIN
Figure 4. Entropy-temperature diagram for Agnes cycle
Figure 3. Entropy-temperature diagram for Mark 9 cycle.
2FeCls(1) = 2FeC12
+
C12 (775 K)
ZFeCl,(c) = 2FeC1,(1) (555 K) Fe,O,
+
8HC1 = FeC12
+
2FeC1,
+ 4H,O(g)
(3H) (4H) (519 K) c 1t5,- 1 )
(1C) Cycles Agnes and C(+5, -1) are identical except for the manner in which oxygen is recovered. The former uses two steps in hydrolyzing MgC12 whereas the latter uses one step, the reverse of the Deacon process for the production of Clz. The entropy change for each step of the three cycles, the total heat absorbed, and the figure of merit for each cycle are given in Table 11. Not included in the table are the two steps common to all, ie., the entropy change on vaporization of water and the entropy of formation. The heat of vaporization was included in the total heat, however. A practical process would utilize some of the heat rejected from reactions 1C for vaporizing the water, which would then reduce the total amount of heat extracted from the high-temperature reservoir. The numbers in parentheses in the heat column have been reduced by the heat of vaporization of water and have been correspondingly increased in the figure of merit column. A diagram of each cycle is presented in Figures 3, 4, and 5. One can see from the diagram that step 2C of the Agnes cycle is responsible for the lowered efficiency compared t o the other two. Interestingly enough the additional heat absorbing step in C(+5, -1) is less costly than the large entropy change in step 1C of Mark 9. Mark 9 may be the most promising of the three mainly because of the favorable combination of gaseous products, although none
I
500
IO00
TEMPERATURE, KELVIN
Figure 5. Entropy-temperature diagram for C(+5, -1) cycle.
can be overly attractive because of the large mass movement to decompose one mole of water. These three cycles are representative of some of the better cycles which have appeared in the literature; yet they tend to dampen the enthusiasm for simple thermochemical cycles. The calculated figure of merit does not take into account imperfection in heat interchange, the work necessary to move material, and the fact that the reacInd. Eng.
Chern., Fundam., Vol. 13, No. 4 , 1974
309
tions will have to be conducted a t a temperature where the A G > 0. The situation is not as bleak as it might appear. Even with a figure of merit of 0.44 which could be reduced to 0.24 in practice, a thermochemical process may require a smaller capital investment than is required for a generator plus electrolyzer. Further, the heat rejected a t 500 K could be used to operate a turbo-generator in order to produce the work required to pump material and operate the plant. Although the efficiency of an engine operating on heat at 500 K is low, this would, nonetheless, improve the overall thermal utilization of the chemical engine. Acknowledgment We wish to thank Darrell W. Osborne for numerous illuminating discussions. Nomenclature Cp = molar heat capacity a t constant pressure, k J / K mol A G = change in the Gibbs energy function, kJ/mol AH = change in the enthalpy, kJ/mol i = runningindex j = total number of reaction steps K = Kelvin temperature n = total number of steps with negative entropy change p = total number of steps with positive entropy change Q = heat absorbed, kJ q = heat rejected, kJ A S = change in the entropy, kJ/K T = temperature, K W = useful work delivered by an engine, Le., work excluding expansion work against the atmosphere; for a chemical reaction the negative of the Gibbs energy change Subscripts and Superscripts C = cold or bottom temperature f = formation from the elements H = hot or top temperature 0 = standard state of 1 atm a t 298.15 K
310
Ind.
Eng. Chern., Fundarn., Vol. 13, No.4, 1974
Abbreviations c = crystal or solid where there might be ambiguity of the state g = gaseousstate 1 = liquidstate Greek Letters 7 = figureofmerit
Literature Cited Abraham, B. M., Schreiner, F., Science, 180, 959 (1973a). Abraham, B. M.. Schreiner, F., Science, 182, 1373 (1973b). Bowman, M., et a / . , Los Alamos Scientific Laboratory, Los Alamos, N. M., personal communication, 1973. de Beni, G., Marchetti, C., Eur. Spectra, 9, 46 (1970). de Beni. G., Marchetti. C., Proceedings of the Symposium on Non-Fossil Chemical Fuels, P 110, Division of Fuel Chemistry, 163rd National Meeting of the American Chemical Society, Boston. Mass., 1972. Chern. Eng. News. 50, 14 (June 26, 1972a). Chem. Eng. News, 50, 16 (July3. 1972b). Euratom Joint Nuclear Research Center, Progress Report No. 3 EUR/C1S/35/73. "Hydrogen Production from Water Using Nuclear Heat." 1973. Funk, J. E., Reinstrom, R . M . , Ind. Eng. Chern., Process Des. Develop.. 5, 336 (1966). Funk. J. E., Reinstrom, R. M.. Proceedings of the Symposium on NonFossil Chemical Fuels, p 79, Division of Fuel Chemistry, 163rd National Meeting of the American Chemical Society, Boston, Mass., 1972. Gregory. D. P., Ng. D. Y . C., Long, G. M., "Electrochemistry of Cleaner Environments," J. O'M. Bockris. Ed., Plenum Press, New York, N. Y.. 1971. Gregory. D . P., "A Hydrogen Energy System," prepared for the American Gas Association by the Institute of Gas Technology, Chicago, Ill., 1973. Hanneman. R . E., Wentorf, R . H., Abstracts, Vol. 18, p 41, 166th National Meeting of the American Chemical Society, Chicago, Ill., Aug 1972. [Chern. Eng. News (staff report), 32 (Sept 3, 1973 ) ] Knoche, F. K.. Schybert. J.. Ver. Deuf. Ing. Forsch , No. 549, 25 (1972) (English translation ORNL-tr-2593). Maugh. T. H.. I I , Science, 178, 849 (1972). Rossini, F. D.. Wagman, D. D., Evans, W. H.. Levine, S . , Jaffe, I., "Selected Values of Chemical Thermodynamic Properties." NBS Circular 500, U. S. Government Printing Office, Washington, D. C., 1952. Wagman, D. D., Evans, W. H., Parker, V. B.. Halow. I., Bailey, S. M.. Schumm. R . H.. NBS Technical Note 270, U. S. Government Printing Office, Washington, D . C.. 1968. Winsche, W. E., Hoffman, K. C., Salzano. F. J.. Science, 180, 1325 (1973).
Received for review F e b r u a r y 25, 1974 Accepted J u n e 14, 1974 Work p e r f o r m e d u n d e r t h e auspices o f t h e U. S. A t o m i c E n e r g y Commission.
