Heat storage by phase transition. Equation of state

Solar Ener~,y Vol. 33, No. 6. pp. s93 604. 1984 Printed in the U.S.A.

(X)38-092X/84 $3.00 + .(X) c 1985 Pergamon Press Ltd.

HEAT STORAGE BY PHASE TRANSITION. EQUATION OF STATE Zt.ATKO STUNI4

Technological Faculty, University "'Djuro Pucar-Stari". D. Mitrova 63b, 78000 Bahia Luka, Yugoslavia (Received 27 April 1983: revision received 18 July 1984; accepted 20 July 1984) Abstract--lncongruent phase transitions accompanied by phase separation frequently cause a deterioration of heat-of-fusion storing systems. This kind of deterioration progresses, cycle after cycle, and is especially damaging in technical devices in which hydrated salts, e.g. CaCI2 . 6H20, Na2SO4 • 10H20, Na2S203 . 5H20, etc., are used as heat storing materials. Processes contributing to deterioration of hydrated-salt systems are analyzed, novel thermodynamic characteristics are proposed to enable unambiguous descriptions, and these are related in an equation of state for triads of characteristics so that any one of them can be calculated if the other two are known. State equations for the three salts mentioned above are represented graphically in three-dimensional diagrams. Predictions deduced from state equations are tested experimentally with systems undergoing rapid (or purely incongruent) and slow (or pseudocongruent) phase transitions (CaCI2 • 6H20 and Na2SO4 • 10H20, respectively). Good accordance between prognosis and experiment is shown.

INTRODUCTION

Present experience shows that incongruently melting materials are of little practical use for phasetransition heat storing [1]. Unfortunately most of the materials available for heat storage at temperatures between 20 and 100°C are hydrated salts which belong to this group. Nevertheless, in spite of the defects stemming from incongruence of melting, there are advantages such as temperature potential and (relatively) large phase-transition heats per unit volume, which continue to interest researchers in the field. Long-term use of heat storing systems based on hydrated salts leads to loss in heat storing capacity due to progressive loss of the form richest in crystal water. Thus a stability problem arises, namely that of keeping these losses to a minimum. Theoretically one may try to obtain a formal congruence of melting in a system based on incongruently melting material. The following devices were tested: (a) addition of agents imparting rigidity to the melt [2], (b) encapsulation [3], and (c) addition of excess water or some other component [4]. The first failed to give satisfactory results, and the second is very expensive, especially because the protective layer thickness (capsular wall) must be less than 1 cm. Generally speaking, however, an inconvenience in any study is that actual decomposition rates of hydrated-salt systems are only known in very few instances [5]. These rates must, of course, depend on the particular properties of the hydrated salt used, on the geometry of the system studied, of the charge-discharge regimen, etc. Practical consid-

erations will show that an incongruently melting material can compete with a congruently melting one (having a small latent heat of melting per unit volume or mass), on the condition that the former's deterioration rate is very low. The main problem in developmental studies, however, is the transfer of laboratory experience to practice, considering the uncertainty of estimates for large numbers of working cycles (1000-5000) based on labol'atory models. Designing heat storing equipment requires welldefined thermodynamic state parameters as well as a knowledge of their interdependence, i.e. a state equation including these parameters. In this paper we try to fulfill these requirements on the basis of our previous investigations of incongruently melting systems [6, 7]. BACKGROUND

When heat is discharged by an incongruently behaving system (initial form, richest in crystal water, denoted as S • aW) two phases separate at the peritectic temperature Tp. One of the phases is a solid and consists of a hydrated salt poorer in crystal water iS • bW, b < a), the other is a liquid containing dissolved salt S, and c moles of water W, per mole of S. The associated chemical change can be shown in schematic form as S •a W ( m e l t ) ~

kt

S • bW(s) + S • cW(soln.) (1)

in which/,~ is the rate constant of solid water-poor hydrate formation. If the heat withdrawal is continued to below the peritectic point, the melt becomes undercooled.

593

594

Z. STuyI~

W h e n the heat-discharge half cycle is terminated and the heat charging started, some of the solid water-poor form will re-form into the original hydrated salt (at Tp or above) by reversal of eqn (1) S • bW(solid) + cW ~+

k2 heat

S • aW(soln.)

2. In this figure, Ro, R~, R2 . . . . denote points in which the system is assumed to be perfectly isolated thermally from its e n v i r o n m e n t . Point Ro corresponds to no which, for a particular hydrated salt A (S • aW) is given as

(2)

Ca N no = ms lOT ~--'~

where k2 is the rate c o n s t a n t of dissolution. A typical phase-transition diagram is shown in Fig. 1. Let no molecules of storage media S be completely dissolved in a moles of water at the beginning of the first half cycle. The n u m b e r of cycles accomplished at any instant may now be considered as a state characteristic and defined as

tt,c i(t) = - - .

(3)

tc

A graphical presentation of time-dependent changes in the heat storing systems is given in Fig.

Point R[ (at the end of the first cycle) corresponds to the n u m b e r of molecules of separated S • bW, which a m o u n t s to ( n - ) c = ms

CA - Cue N 100 p~s "

L)

Cuc N ( n + ) , x = no - ( n - ) ~ = r n ~ - - - 100 p~s"

35

ell e E

,r

Tp

30'

I I I I ~5 I I I I I I

Tf = 20

45

ef

L--L+ Cuc

CpC A

Weight

(5)

Finally, point R~ corresponds to the n u m b e r of molecules of S • a W at the end of the first cycle, which is

40

o

(4)

1__ ~5 =/. CaCIq. ( S )

Fig. 1. Part of a phase diagram of CaCI2 . 6H20 (S = CaCIz).

6O

(6)

Heat storage by phasetransition

595

U

% % %

I I I

I

/

<2

,21

I

/ I

e~

o e-

% % oc

~E I I I I

5~

I

o~

I

~R _E

~

E' 7

~ol

g °U]

°u

,,,,,,

Z

LU E3

w

I,li

O~ Z

0 k03

~U

/

~u

m

C ri & ~r

596

Z. STUNI~"

The time course of changes in n and their relationship to pertinent magnitudes in a series of cycles are s h o w n in Figs. 3(a) and (b). At this stage let a new state characteristic be introduced: the relative latent phase-transition heat ~p (termed "coefficient of true phase-transition reversibility" in a previous paper [5])--or. alternatively, the s y s t e m ' s deterioration degree denoted by the same symbol. This characteristic is defined. for each cycle, in three ways. Firstly, by latent heat of a phase transition, e.g. ~pt -

(L*h Lo

{7)

S e c o n d l y , ~ is defined as the ratio of numbers of

molecules, e.g. (n + )l,c ~p~ - - H0

(8)

which may, finally for a chemical pure system, be rewritten with regard to eqns (4) and (6) as ~l -

Ctlc

CA

(9)

As both C,,~ and CA are constants, ~p~ is a system parameter and one can denote it by a particular symbol e. If the separation of solid (S - bW) and liquid phases advances along the curve connecting points

p-

TIME

1

CA

1-

Cuc cA

o

--// 47 o

;-o

n - c / n . : f (t)iz~Tue,m0~<:Tcr - T f

c

Cf CA

t UC

~ r ~

tcr

tG

Fig. 3. (a) Time dependence changes in the number of molecules a solid salt hydrate forms. (b) Cooling curve for a latent heat storage system.

597

Heat storage by phase transition P a n d Cf (Fig. 1), the solubility coefficient v of S • b W in t h e melt c a n be e q u a t e d to a ratio of differences AC v = -- . AT

(10)

P h a s e d i a g r a m s for N a 2 S 2 0 3 " 5 H 2 0 d r a w n with u n p u b l i s h e d d a t a p r o v i d e d b y K i m u r a ( p r i v a t e comm u n i c a t i o n ) , CaCI2 • 6 H 2 0 [8], a n d Na2SO4 • 1 0 H 2 0 [9] s h o w t h a t v = A f ( T ) is a p p r o x i m a t e l y linear. T h e r e f o r e , C ~ is linearly d e p e n d e n t o n the temp e r a t u r e d i f f e r e n c e A T,,~

c a n also c a l c u l a t e

F o r the s e c o n d cycle, t h e r e f o r e , the following relationships can be written: (n +)2.~ = n o [ e - ( l

v A T ....

v

~ Tu~

CA

(12)

[~'A

With r e g a r d to a n o t h e r e x p r e s s i o n o f ~ r e p o r t e d in a p r e v i o u s p a p e r [5], i.e.

(20)

i i )i.c = no

~

(1 -

-

e) ~

] (e h ) k

(22)

/,: I

(n

+)i.h

[ 1 --

= no

(1 -

e) X ~

'

(eX) k ~

]

.

(23)

k=l

T h e s u m in the s e c o n d t e r m within b r a c k e t s in eqn (22) is t h a t o f the first n t e r m s o f a g e o m e t r i c a l series S,, -

1

(X e)"

1

--

h~

n=l,* = exp (-

(21)

and then generalized

(11)

T h e relative first-cycle latent p h a s e - t r a n s i t i o n heat is, t h e r e f o r e Cp e = --

- e) h e ]

(n+)2.h = n o l l -- (1 -- ~)X + (1 -- ~ ) h : e ]

(n

C,~ = C o -

(19)

( n * h . h = no [I - h(1 - ¢)1.

3.

i

(24)

(13)

kjtc)

so t h a t e q n (22) c a n be w r i t t e n as the rate o f c o n s t a n t of w a t e r loss in the t r a n s i t i o n f r o m S • a W to S - b W c a n b e c a l c u l a t e d ( n + k ~ = no

1

1 -e 1 - x~[l

} - (h~Y]

.

(25)

, k, = zln

~AA -

V-~A]

"

(14)

If t h e r e is n o c o m p l e t e r e g e n e r a t i o n o f S • a W in the s u b s e q u e n t c h a r g i n g half cycle, the following r e l a t i o n s h i p holds: (n + )ix = n o -

)ix.

i (n

(15)

In this c a s e e q n s (4), (5), a n d (9) m a y be u s e d to c a l c u l a t e the C-value for a n y cycle ¢i = ( n + ) i . J n o = 1 -

i ( 1 - e).

e).

(17)

D u r i n g e a c h h e a t - c h a r g e i n t e r v a l th, t h e r e is a cons i d e r a b l e c o n v e c t i v e flow in t h e melt, so that s o m e o f t h e solid p h a s e (S • b W ) h a s an o p p o r t u n i t y to r e h y d r a t e a n d d i s s o l v e (eqn (2)). T h e t u r n o v e r is given, e.g. for the first cycle, by (n-)l.h

= (n-h.c exp (-k2

to).

¢/ = 1

(18)

By s u b s t i t u t i n g the s y m b o l h for the e x p o n e n t i a l t e r m a n d u s i n g the e x p r e s s i o n t h e r e b y o b t a i n e d o n e

1 --

- 1 -

,q-

k~

[1 - (X eY].

126)

P a r a m e t e r s e a n d X d e p e n d solely on the s y s t e m p r o p e r t i e s (k~, k2) a n d the s y s t e m ' s i n t e r a c t i o n with its e n v i r o n m e n t (t~, th). O n e c a n d e s i g n a t e the product h = +

(16)

E q u a t i o n (16) allows the c a l c u l a t i o n o f the maxim u m n u m b e r o f useful c y c l e s p e r m i t t e d with a syst e m c o n t a i n i n g a p a r t i c u l a r h e a t storing material, i.e. the n u m b e r of c y c l e s p o s s i b l e b e f o r e @ r e d u c e s to z e r o imax = 1/(I -

A c c o r d i n g to e q n s (16) and (25), the ~ - v a l u e in the ith cycle is t h e n

(27)

as the relative rate o f d e t e r i o r a t i o n o f the s y s t e m . If h e a t i n g a n d cooling i n t e r v a l s h a v e the same l e n g t h t~ = th = t, t h e n + = exp t-kit(1

+ kx/k.)]

(28)

a n d ¢ is a state c h a r a c t e r i s t i c . T h e t h r e e s t a t e c h a r a c t e r i s t i c s ¢, i, a n d ¢ c a n n o w be u s e d to e s t a b l i s h a state e q u a t i o n ¢i = 1 -

((1 - e)(l - ¢")/(I - ¢))

(29)

or in m o r e general f o r m F ( ~ , i, tb) p , T~F = O.

(30)

A t h r e e - d i m e n s i o n a l g r a p h r e p r e s e n t i n g the state e q u a t i o n o f Na2CO3 • 1 0 H 2 0 is g i v e n in Fig. 4.

598

Z. STUN[(~"

However, as the plotting of curves on the thermodynamic surfaces is generally cumbersome, the use of a two-dimensional (reduced) representation ~i vs i is recommended for practical purposes.

DISCUSSION

Incongruent ( ~(ast') phase transition Heat storing systems based on this type of phase transition are characterized by their inability to fulfill the process outlined in eqn (2) because there is no possibility of removing S • bW instantaneously at the termination of the process. Nevertheless, such systems may be useful if dissolution of S • bW can be neglected, e.g. because of a practically instantaneous sedimentation of this product (its crystals have a much larger density than the melt), or because of a poor solubility in the melt. Incongruency is indicated by ~.-values close to unity (or q~-values close to ~). To illustrate the validity of a state equation for such systems a ~cxp, ~ c ~ diagram f o r C a C l 2 • 6H20 (Fig. 5, line a) using data reported by Carlsson et al. [8] has been plotted. In calculating ~c,,~c (using eqn (29)) a mean value of 0.98 was taken for ~,, assuming that only 2% of the tetrahydrate formed during a cycle goes into solution. Applying a least-square fit to data of the ~cxp with respect to ~a~c, one can determine the factor of the t-distribution [10]. The calculated factor t-distribu-

i

Fig. 4. T h r e e - d i m e n s i o n a l graph o f e q n (29) (see text) with p a r a m e t e r s for Naz CO3 . 10H20.

O

.8 J O U

y

.V

-

U

go

.6

GID

HgO

(ref9)

Nags 0Lt.~10 I~0 .5

•

.4

t

.5

I

.6

(refl 6 )

new thickener Crystalhabit mOdif=er

~

'

.7

I

.8

I

.9

I

1.

~0ex p. Fig. 5. L e a s t - s q u a r e fit analysis of eqn (29) for experimental results for (a) CaCla . 6HzO, and (b) Na2SO4 • 10H20 provided from Ref. [8] and Ref. [I ll.

599

Heat storage by phase transition tion (r = 0.966) is 17.025, while the limit of the critical region (for 23 data) is 2.831. That way there is an excellent, linear dependence of experimental and calculated data for values of q~ in accord with eqn (31) (A = 0.588 and B = 0.546) ~¢alc

-

-

A '.Pexp + B.

(31)

The obtained values for A (A ¢ 1) and B (B ¢ 0) are probably the result of different experimental conditions in the measurement of latent heat of an incongruently and a pseudocongruently phase transition. In addition to that, for an investigated heat storage system it is possible, in monitored cycles, to obtain more than one value of latent heat, therefore, one must take into consideration that the reported value is the arithmetic mean of a possible value. The three-dimensional (~p, i, +) state equation for CaCI2 • 6 H 2 0 is represented graphically in Fig. 6. The dashed line on the hindmost thermodynamic surface corresponds to h = 0.98 and agrees fairly well with Carlsson's [8] results. Mathematical analysis of data for Na2SO4 1 0 H 2 0 [! 1[ is shown on Fig. 5, line a, b. In this case

there is obtained very good agreement between experimental and calculated values for q~. The indicated factor t-distribution was 10.807 (r = 0.938), while the limit of the critical region was given as 2.921 (for 20 data). The values for A (eqn (31)) are very near unit (A = 1.132) and the indicated values for B (eqn (31)) have a tendency towards zero. It is important to mention that the values for latent heat of the incongruent and the pseudocongruent phase transitions were obtained in the same experimental way. Another three-dimensional diagram (Fig. 7) illustrates the behavior of N a 2 S 2 0 3 • 5H20, one of the most often used ones in heat storage. A comparison of Figs. 6 and 7 shows that the area of the thermodynamic surface depicted for N a 2 S 2 0 3 - 5 H 2 0 is almost double that of CaCI2 • 6 H 2 0 , which is due to a much larger ~-value of the former. The large ~value makes N a 2 S 2 0 3 • 5 H 2 0 better suited for multicycle utilization than CaCI2 - 6H,O.

Pseudocongruent ('slow')phase transition Sodium sulfate decahydrate (Glauber's salt) is an especially interesting heat store as it enables energy to be stored at high density [12-14]. However, like

#.s .6

.7

.8

.6

l .4

eZ'--- ~,

% %

C a C 1q-6 H~O

~0/

40 /

OM/

u,.l/

i Fig. 6. Three-dimensional graph of eqn (29) (see text} for CaCI2 • 6H20.

Z. S I'UNI("

600

i

Fig. 7. Thermodynamic surface tk~r N a 2 S 2 0 3

most hydrated salts, this material melts incongruously, and heat storing systems based on its use deteriorate rapidly [15]. This disadvantage might be o v e r c o m e by suitable additives. Telkes studied the influence of several thickening agents intended to make the melt of Na2S()4 • 10H20 with suspended particles more h o m o g e n o u s [161. T o evaluate these results a ~p, i diagram is presented in Fig. 8 showing the influence of attapulgite clay, a gel-forming additive (curve I ). F u r t h e r m o r e , c u r v e 2 in the same diagram represents the influ-

" 5H20.

ence of Na2B407 • 10H20 added to prevent undercooling, and curve 3 shows the b e h a v i o r of Glaube r ' s salt without additives, a system in which ~, was assumed to be 0.98 (the same as for CaCI2 ' 6H20). A c o m p a r i s o n of curves 1 and 3 shows that attapulgite clay greatly reduces the deterioration rate of Na2SO4 • 10H20. Three more curves plotted in Figs. 8(a)-(c), fit the data for the interval between the first and tenth cycle, the tenth and one-hundredth cycle, and those for cycles beyond the onethousandth, respectively. Equation (29) was used

a

6

\, ~4

\\,

2

\ 2

\

OD

\ \

10

100

1000

Fig. 8. Dependence of relative phase-transition heat '4 on number of heat charge-discharge cycles i for Na2SO4 " 10H20.

Heat storage by phase transition

601

o

ooY- I-'6

4

2

O(

I

I

I

]

I

2

4

6

8

10

i

I

12

100

Fig. 9. Dependence of regeneration degree h of Na2SO4 " 10HzO with respect to number i (cf. curve 1. Fig. 8).

---C---

~-f(~,)

u

I

I

.5

1

%

4

6

, m m .100 Fig. 10. ~, ,k- a n d tp, 6 2 - d i a g r a m f o r N a 2 S O 4 • 1 0 H 2 0 .

8

602

Z . STUNIC'

[ll]. The formation of these crystals is consistent with the decline in performance with cycling, since a large crystal would take longer to dissolve than the same mass of material in the form of fine powder. The rate of dissolving of the S - bW, or number h is roughly proportional to surface area of the large crystals [17]. Results of applying the least-square fit to the data taken from Ref. [11] for latent heat (relative) q: particle size 8 and data for h (according to eqn (32)) is shown on Figs. 10 and 11. It is seen that the change of relative latent heat q~with respect to h is nearly as 82 (thus proportional to the surface area); it is found that a simple correlation can be obtained for this dependence hi = 0.1282 - 0.05.

(33)

This result suggests that the crystal size of the Na2SO4 must be controlled in order to decrease the number h (or relative rate of deterioration of the system 0) and, finally, to improve performance of the material with cycling. 0

2

4

6

M i n i m u m value of" relative phase-transition heat

3 ~ , m2.100

(~m~n) If the heat discharge of a system is conducted very slowly, the system remains practically under equilibrium conditions, and the reaction eqn (2) can go almost to completion. If S - aW is regenerated at all (during charge periods), then q~ > 0 regardless of the number of previous cycles. Furthermore, the interdependence of the degree of regeneration h, and the relative latent heat of phase transition e (i.e. the value of their product 0, see eqn (27)) plays a crucial role. It is easily demonstrated that, for i tending to infinity, the following relationship holds

Fig. 11. h, 82-diagram for Na2SO4 . 10H20.

to obtain curves a-c. Despite the wide dispersion of q>values (q~m0 = 0.76, q~oJ = 0.63), the rate constant k2 (represented by h) increases in a regular manner with increasing i (Fig. 9). The following empirical equation can be obtained by the method of least-square fit hi = 0.86(1 - exp (-0.022i) - 0.16 e x p ( - 2 E - 3i2)).

(32)

(lim ~i), . . . . . t = (e - +)/(1 - 0)

This suggests that some physical transformation is occurring in the system with prolonged cycling. Subsequent analysis of the sample revealed the presence of large, well-formed crystals of Na2SO4

(

=

L~min.

Figure 12 shows the relationship of ~ and i for a sodium sulfate decahydrate system containing ad-

%%%

JB

% % O0

a

%(

b --..J

.6

4

I

Fig. 12. q~, /-diagram for

6

7

x 100

• 10H20 in the presence of modifiers (cf. Ref. [1 IlL Curve a, new modifier: curve b, crystal habit modifier.

Na2SO4

(34)

Heat storage by phase transition

603

\ill \/// 4

0

.2

.4

.6

.8

1

Fig. 13. Dependence of minimum latent phase-transition heat ~p,+,+,on variables • and ~,.

ditives specified in Ref. [11] to ensure a c o n s t a n c y of latent phase-transition heat. Curve a shows that an equilibrium situation is reached after 200 cycles by using ' n e w t h i c k e n e r ' as an additive. H a v i n g an exceptionally high e-value (e = 0.9972), this system finally attains a large relative phase-transition heat despite a low degree o f regeneration (}t = 0.9929). The smallness of fluctuations around ~p,,+, justify its introduction as a reference magnitude: moreover, ~Pm+nis i n d e p e n d e n t o f / a n d depends solely on e and X. A n o t h e r additive, 'crystal habit modifier', causes the system to b e h a v e as shown by curve b. In this case the e-value is s o m e w h a t smaller (~ = 0.9950), the X-value is practically the same (X = 0.9925), and ¢Pmin lower than in the f o r m e r case. In view o f the r e m a r k a b l y high ~m+, values and the low degree of regeneration (about I%), it may be a s s u m e d that the p r o c e s s e s involving G l a u b e r ' s salt [11] a d v a n c e very slowly, which raises the question about the value of characterizing with just the heat accumulation. Finally, eqn 134) allows a stable working regimen

(Pro+n) to be anticipated for any heat storing material, A set of c u r v e s illustrating this point is nresented in Fig. 13. The ~P,~m values were determined for a given g e o m e t r y and c h a r g e - d i s c h a r g e regimen. A still more detailed analysis of regeneration of various materials is desirable, especially for those which only few data have been reported so far.

NOMENCLATURE A, B

CA, CF, Cp Cu~ AC i k ~+kz Lo L+

slope of the regression line and the 3,-intercept m a regression analysis. percentage of S at point A, F, and P on Fig. I percentage concentration of S. aW in liquid phase cooled on temperature TL,c (point T in Fig. [) concetration difference number of cycles rate constant of water-poor hydrate IS • bW) formation and dissolution hypothetical latent heat of a 'quasislatic' phase transition actual latent heat

604

Z. STUNI(" N no n÷,n

S S . aW S . bW AT tc

th lct-

tt,c tt£~;

8

v

~calc+~cxp ~min

+

Avogadro's number number of molecules of S • aW at the beginning of the first cycle number of molecules of S - aW and S • hW. respectively sample correlation coefficient in a regression analysis anhydrous salt hydrated salt richest in crystal water hydrated salt poorer in crystal water temperature difference time interval during which the heat sturing system changes from fully charged to fully discharged state time interval of the opposed (in relation to t~) change of state length of the period during which crystallization of S - aW proceeds total duration of heat discharge length of the period of undercuoling crystal size relative latent phase-transition heat in first cycle regeneration degree of S. bW for an~. cycle and for a number of cycles tend to infinity molecular weight solubility coefficient of S . hW relative latent phase-transition heat
REFERENCES

I. F. Relier, Physical and chemical processes fur latent heat storage at low temperatures. Cited from ('hem. Abstr. 95, 100612: Alternative Ener~,,y Sources' 1979 2(11, 341(1981). 2. S. Furbo, Heat storage with an incongruently melting salt hydrate as storage medium based on the extra

water principle. Therm. Storage Sol. Energy Proc. Int. TNO-Symp. 1980, p. 135 (Pub. 1981). 3. E. Van Galen and C. den Ounden, Development of a storage system based on encapsulated P.C. materials. Soon 2 (Two), Proc. Int. Sol. Energy Soc. Silver Jubilee Congr., Vol. 1, p. 655 (1978). 4. S. Furbo, Investigation of heat storages with salt hydrates storage medium based on the extra water principle. Comm. Eur. Communities/Rep/Eur/6646, Pt. 2 (198(I). 5. Z. Stuni6, V. Duri~kovi~+ D. Majstorovi~ and V. Buljan, Thermal study of multicycle melting and freezing of sodium thiosulfate pentahydrate. J. Chem. Tech. Biote~+hnol. 32, 393 (1982). 6. Z. Stuni~. V. Duri~kovi~ and M. Krki6, Thermal storage: nucleation of melts of inorganic salt hydrates. Kern. Ind. 1978 (12), 661. 7. Z. StuniC V. Duriekovi~ and Zd. StuniC Thermal storage: nucleation of melts of inorganic salt hydrates. J. Appl. Chem. Biotechnol+ 28, 761 (1978). 8. B. Carllson, H. Styrene and G. Wettermark, An incongruent heat-fusion system--CaCl2 • 6HzO--made congruent through modification of the chemical composition of the system. Solar Energy 23, 343 (19791. 9. S. Cantor, DSC study of melting and solidfication of melt hydrates. Thermochim. Acta 33, 69 (19791. 10. G. W. Snedecor and W. G. Cohran, Statistical Methods, p. 144. Iowa State University Press, Ames, Iowa (19671. I1. S. Marks, Thermal energy storage using Glauber+s salt: improved storage capacity with thermal cycling. Proc. lntersoc. Energy Convers. Eng. Conf., Vol. 15 (11+ p. 259 (19801. 12. M. Telkes, A review of solar house heating. Heating Ventilating 46, 60 (1949). 13. M. Telkes, Solar energy storage. A S H R A E Trans. 80(II), 38 (19741. 14. J. W. Hodgins and T. W. Hoffman, The storage and transfer of low potential heat. Can. J. Technol. 33, 293 (1955). 15. S. Marks, An investigation of the thermal energy storage capacity of Glauber's salt with respect to thermal cycling. Solar Energy 25, 255 (1980). 16. M. Telkes, Thixotropic mixture and method of making same. U.S. Pat. No. 3,986,969, 19 October (1976). 17. V. N. Stabnikov, V. D. Popov, V. M. Lysjanskii and F. A. Redyko, Processy 1 Apparaty Pishevyh Proizodstv, p. 607. Prishch. Prom. Moscow (19761.