UNITED STATES DEPARTMENT OF THE INTERIOR 

GEOLOGICAL SURVEY

Heat capacity and thermodynamic properties of equilibrium sulfur to the 

temperature 388.36 K, and the heat capacity of Calorimetry Conference coppera

by 

Bruce S. Hemingway

U.S. Geological Survey Open-File Report 99-324

a This report is preliminary and has not been reviewed for conformity with 

U.S. Geological Survey editorial standards
Abstract

The heat capacity of specially prepared orthorhombic sulfur has been 

measured in a low-temperature adiabatic calorimeter. Measurements from T ~ 6 

K to near the melting temperature transition at Tfug = 388.36 K are reported 

for equilibrium sulfur: for the orthorhombic modification from T » 6 K to the 

temperature of the orthorhombic-to-monoclinic transition Ttrg = 368.3 K, and 

for the monoclinic modification from Ttrs to Tfus . The molar entropy AjS^/R and 

molar enthalpy function A^.H^/RT for orthorhombic sulfur calculated from this 

data set are (3.843 ± 0.010) and (1.776 ± 0.005), respectively, where T = 

298.15 K, T 1 - 0, and R = 8.31451 J-K^-mol' 1 . Four measurements of the, 

enthalpy of the orthorhombic to monoclinic phase transition were made with 

three samples. At Ttrs , the average value for the enthalpy of transition AcrsH° 

is (401.3 ± 0.8 J-mol" 1 ) . The heat capacity of the orthorhombic phase is 

given by the equation: Cp<n/ (J-K^-mol-1 ) = 15.830 + 0.023036 (T/K) for the 

temperature interval (290 to 368.3) K, and that of the monoclinic phase by 

Cp , m/ (J-K^-mol- 1 ) = 11.8498 + 0.035197 (T/K) for the temperature interval 

(368.3 to 388.36) K. Previous determinations of the heat capacity of sulfur 

are discussed in the text.

1. Introduction

The reliability of thermodynamic property measurements can be jeopardized 

by the presence of undetected impurities in experimental materials. Accordingly, 

in the most careful calorimetric investigations, great efforts are often expended 

on the purification and analysis of substances to be studied.

Almost 40 years ago, Murphy et al. (1) devised a method for the preparation 

of high-purity sulfur to be employed in measurements of its boiling temperature, 

a fixed point on the International Temperature Scale. A portion of this material 

was used by West 121 in a determination, by adiabatic calorimetry, of the heat 

capacity of sulfur at room and superambient temperatures. Samples of sulfur 

prepared by the same technique and at about the same time were used by 

Montgomery (3) in low-temperature heat-capacity calorimetry (it is not clear from 

Montgomery's thesis whether his specimen was from the same batch as West's), and 

as a secondary standard (designation, USBM-Plb) in combustion calorimetry of 

organo-sulfur compounds. (4)

Seven years ago, Susman et al. 15) pointed out that previous measurements of 

the physical properties of sulfur had been "seriously compromised" by the 

unsuspected presence in research specimens of such impurities as carbon, 

hydrocarbons, H2 S, H2 SX , sulfone, sulfoxide, and sulfonic and sulfinic acids. As 

preamble to their successful efforts to prepare sulfur with a targeted mass 

fraction of impurity close to 10~ 6 , they analyzed other specimens of putative 

high purity. They found, inter alia, that the USBM-Plb secondary standard 

contained mass fraction 3.1-10"4 of contaminants and, in harmony with that 

observation, later calorimetric measurements IS) showed a statistically significant 

difference between the massic energies of combustion in fluorine of USBM-Plb and 

sulfur with mass fraction impurity of 5-10~s from Susman et al. It may be 

inferred that other specimens prepared by the method of Murphy et al. could have 

had levels of contaminant similar to that of USBM-Plb, and that the mole 

fractions of liquid-soluble, solid-insoluble impurity, 1.3-10"5 and 7-10' 5 , 

claimed by West 12 ' and Montgomery'31 on the basis of the "freezing-point 

depression", may be too low. It is impossible to deduce the molar mass of
impurity and, thus, the corresponding mass fraction for comparison with the other 

samples. Contamination of West's and Montgomery's specimens solely by H2 S04 , for 

example, would imply a mass-fraction impurity of ~ 4-10'3 .

An earlier investigation by Eastman and McGavock (7) described the 

purification of commercial sulfur by recrystallization from CS2 , which was then 

removed by pumping. Although residual CS2 was stated to be less than mass 

fraction 10" 5 , we do not believe, in light of the elaborateness of subsequently 

developed efforts for the removal of organic matter from sulfur, that Eastman and 

McGavock's procedure could have yielded material of acceptable quality. Those 

authors gave no additional analytical details.

Berezovskii and Paukov(8) took care to acquire high-purity sulfur for use in 

their low-temperature calorimetric studies. It appears, however, that their 

specimen may have contained mass fraction 1.1-10" 3 of Si02 ; other (nonmetallic) 

contaminants could also have been present, but no analytical results are given 

for C, H, 0, or N.

In light of the preceding observations, and the key role played by the 

thermodynamics of sulfur in many areas of science and technology, we thought it 

advisable to remeasure the low-temperature heat capacity of equilibrium sulfur, 

using the very pure, fully characterized material provided by Susman et al. , 

which contains a factor of 10, perhaps even 100, less impurity than the other 

specimens described in the preceding paragraphs. (This work was done in 

cooperation with Malcolm W. Chase, and P. A. G. O'Hare, National Institute of 

Standards and Technology (NIST), Physical and Chemical Properties Division, 

Gaithersburg, MD 20899, U.S.A., who arranged for the transfer of the sulfur 

sample to the U.S. Geological Survey, requested this study, received copies of 

the data base, and reviewed this report. This report contains a description and 

analysis of the heat capacities measured in the Thermodynamic Properties 

Laboratory of the U.S. Geological Survey and transferred to NIST.)

2. Material

Prior to the present work, Susman et al. 's (5) sample had been protected from 

exposure to the atmosphere at all times since it was prepared and analyzed. Its 

composition and chemical analyses have been presented in detail; (6) total 

impurities amounted to mass fraction 5-10"6 . The unit-cell dimensions were 

calculated from 41 diffraction lines using a Guinier-Hagg1" X-ray camera with a 

copper target and standard reference material Si (SRM 640) as an internal

f Certain commercial equipment, instruments, or materials are identified in this 

paper to specify adequately the experimental procedure. Such identification does 

not imply recommendation or endorsement by the U.S. Geological Survey or the 

National Institute of Standards and Technology, nor does it imply that the 

materials or equipment are necessarily the best available for the purpose.

standard. The unit cell parameters and volume were: a = (1.0454 ± 0.0002) nm; 

b = (1.2870 ± 0.0003) nm; c = (2.4472 ± 0.0005) nm; and V = (3.2927 ± 0.0009) 

nm3 . Within the normal temperature range of low-temperature calorimetry, sulfur 

undergoes two transitions: from orthorhombic to monoclinic modifications at T = 

368 K, and from monoclinic to liquid at T ~ 388 K, both of which are presumably 

influenced by impurities.
3. Calorimetric methods

Measurements of the standard molar heat capacities at low temperature 

employed the intermittent heating technique with the adiabatically shielded 

calorimeter and methods described by Robie and Hemingway 191 and Robie. 1101 A 

calorimeter with an internal volume of about 30 cm3 was used. Calorimetric 

temperatures were determined with a Minco model S1059-1 platinum-resistance 

thermometer. This thermometer (R0 = 100.014997 Q) was calibrated by the 

Temperature Measurements Section of the U.S. National Institute of Standards and 

Technology on IPTS-68 between T = 13.8 K and T = 505 K, and between 4.2 K and 

13.8 K on a provisional temperature scale used in the laboratory ._(11) The 

calorimeter contained a mass of 27.2366 g of sulfur.

The calorimeter was calibrated with Calorimetry Conference reference 

material copper; the results obtained for the heat capacity of copper agreed with 

those published earlier [12] . In 1965, the Calorimetry Conference made available 

a high purity copper sample to be used for interlaboratory comparisons of heatcapacity measurements'131 . The sample received by the U.S. Geological Survey bore 

the designation T7.2, was in the form of a right-circular cylinder 3.18 cm in 

diameter, 5.34 cm in length, and was 376.2 g in mass. Sample preparation and an 

earlier set of heat-capacity measurements were presented in an earlier study[111 . 

For this study, the copper mass was 242.5746 g (in vacuo).

In 1987, Martin 1121 published a reference equation for the heat capacity of 

copper from T = 20to320K that was based upon measurements from his laboratory. 

This equation superceded an earlier reference equation developed by Martin that 

used the copper data given in reference [11] and earlier data from Martin's 

laboratory. We believe that Martin's revised equation for copper when combined 

with the equation for copper for temperatures at and below T = 20 K given by 

Osborne and others [13] provides the best reference heat capacities for copper. 

Between T = 30 and 320 K, our observed heat capacities differ from the reference 

values by less than 0.1% (generally less than 0.05%), except at about T = 60 K 

where one value differs by 0.25%. Between T = 13.5 and 30 K, our values differ 

from the reference values by about 0.5% or less. At lower temperatures, 

deviations of I to 5% occur and reflect the rapid decrease in sensitivity of the 

platinum resistance thermometer as the absolute 0 of temperature is approached. 

Accordingly, the calorimeter was deemed to be functioning properly.

Our heat capacity measurements for copper are listed in table 1, in the 

chronological order of measurement. The heat capacities of series 1 and 2 were 

smoothed separately using an 11th order polynomial. The smoothed results were 

integrated to obtain the entropy difference for the temperature interval of T = 

60 to 320 K yielding 31.137 and 31.139 J mol' 1 K' 1 , respectively for series 1 and 

2. Smoothed values from Martin's reference equation were similarly integrated 

yielding 31.136 J mol' 1 K' 1 . For the temperature interval T = 6 to 60 K, the 

entropy calculated from our smoothed heat capacities is 3.713 J mol'1 K" 1 and is 

compared to the value calculated from the reference equations of Martin and 

Osborne and others of 3.718 J mol" 1 K' 1 , a difference of -0.13%. For the 

temperature interval T = 6 to 320 K, the entropies calculated from our data 

differ from that calculated from the reference equations by 0.01%.

4. Results for orthorhombic sulfur

Low-temperature heat-capacity results for orthorhombic sulfur are listed 

in chronological order in table 2 . The values were smoothed by means of a cubic
spline: Cp im (T) = a + b-T + c-T2 + d-T3 . Because of scatter, the experimental 

heat capacities at T < 10 K could not be fitted as a smooth function of T. This 

may reflect the effects of partial adsorption of some of the He exchange gas at 

the lowest temperatures. Accordingly, for temperatures between T - 0 and 10 K, 

values of Cp\ m were calculated at 1 K intervals based on the assumption that 

sulfur, a non-metal, obeyed the relation: Cp jtn = A-T3 . The corresponding Cpim 

against T curve merged smoothly with the cubic spline fit at T = 10 K. A 

deviation plot in figure 1 compares the experimental and smoothed results; the 

latter are also shown in figure 2, as a function of temperature.

Values of the thermodynamic functions of orthorhombic sulfur from T - 0 to 

T = 368 K, calculated from the smoothed Cp /ms, are listed in table 3. The entropy 

A£S;/R = (3.843 ± 0.010) and enthalpy function A?,H;/RT = (1.776 ± 0.005), where 

T = 298.15 K and T 1 - 0. Smoothed heat capacities for temperatures between 290 

K and 368.3 K were fit with the equation:

Cp , m/(J-K^-mol'1 ) = 15.830 + 0 . 023036 (T/K) , (1) 

with an average absolute deviation of +7 10~4 -Cp jtn .

5. Results for monoclinic sulfur

Conversion of orthorhombic to monoclinic sulfur proceeds slowly near the 

transition temperature, as noted in earlier studies. <2 ' 3 - 7 ' Therefore, for the 

Series 2 and 4 (table 4) experiments, our sample was heated to T = 380 K (where 

conversion is facile) and then cooled rapidly (to the starting temperature of the 

measurements) in order to freeze in the monoclinic modification.

Experimental heat capacities for monoclinic sulfur are listed in table 4 

in the chronological order of measurement. The results were fit with the 

equation:

Cp>m/(J-K-1 -mol-1 ) = 11.8498 + 0 . 035197 (T/K) , (2) 

with an average absolute deviation of ±7 10" 4 Cp/m . This equation is valid for the 

temperature interval 368.3 K to 388.36 K, and smoothed heat capacities derived 

from it were used to compute the thermodynamic quantities for monoclinic sulfur 

listed in table 3. Deviations of the smoothed heat capacities from the 

experimental results are shown in figure 1. The smoothed data are also shown in 

figure 2 as a function of temperature.

6. Enthalpy of transition: orthorhombic to monoclinic sulfur

Four measurements of the enthalpy of transition were made with three 

samples of sulfur. Experimental details are given in table 5. Because of the 

slow equilibration of the monoclinic phase at temperatures below 375 K, 

measurements were made of the enthalpy from T < 368.3 K to T > 375 K. These 

values were corrected for the heat capacity of the orthorhombic phase at T < 

368.3 K and the monoclinic phase at T > 368.3 K, on the basis of equations (1) 

and (2).

7. Discussion

No evidence has been found in our measurements of the heat capacity of (3- 

sulfur for the transition in the temperature region between 368.3 K and 374 K 

suggested by West. 12 ' Our conclusion is in agreement with that of Montgomery. !3) 

West indicated that his sample was converted to the monoclinic form at a 

temperatures greater than 374 K, from which he cooled it to lower temperatures,
where measurements were begun. Identical procedures were followed in the present 

study. The first measurement of series 5 is significantly higher than 

measurements at similar temperatures in series 4. However, this measurement was 

followed by measurements that are consistent with the earlier series without 

indication of a transition.

Difference in sample response could mean that an intermediate structure 

develops on heating. At T < 375 K, change from orthorhombic to monoclinic sulfur 

proceeds slowly. At T > 375 K, transition is complete in a few minutes or less. 

West's observations suggest that the transformation from the orthorhombic to the 

unknown monoclinic form requires substantial time, which may vary with the purity 

of the sample. Currell and Williams [14] reported a double peak in differential 

scanning calorimetric heat capacities for flowers of sulfur that occur in the 

temperature interval identified by West. These authors attribute the first peak 

to the a-3 transition in sulfur, and the second peak to the melting of chain 

structure sulfur. West was aware of the possible formation of chains of sulfur 

instead of the ring structure of monoclinic sulfur and took precautions to avoid 

development of sulfur having the chain structure.

Four studies have presented structural data for 3-sulfur, two provide unit 

cell information [15 ' 16] and two provide x-ray diffraction data. 117 - 181 The unit cells 

differ in both axial length and in the size of the 3-angle. The space groups 

were given as P2I /c [15] and P2I /a [161 . The x-ray diffraction patterns of Taylor and 

Rummery 1171 and Pinkus et al. [18] were based on the unit cells of Templeton et 

al. [1S] and Burwell [16] , respectively. The calculated d-spacings differ and led 

Taylor and Rummery to conclude that the data of Pinkus et al. were in error.

Sample preparation for the materials used in the structural determinations 

differed and may provide some insight into the question of a possible transition 

in the stability field of monoclinic sulfur. Burwell crystallized sulfur from 

the melt and held the sample at T = 376 K during the x-ray analysis. Pinkus et 

al. used a heating stage that melted a pure orthorhombic sulfur sample and the 

diffraction pattern was "determined immediately on solidification." Taylor and 

Rummery heated their sample in a heating camera through the a-3 sulfur transition 

to about T = 373 K and determined the diffraction pattern. Taylor and Rummery 

observed anomalous intensities that they attributed to recrystallization of the 

sample. Thus Burwell and Pinkus et al. synthesized 3-sulfur in the temperature 

interval where heat-capacity measurements demonstrate rapid conversion to the 

monoclinic structure. Taylor and Rummery synthesized 3-sulfur in the temperature 

region where conversion is anomalously slower as compared to conversion at the 

higher temperatures. Templeton et al. synthesized their sample as a by-product 

of a reaction in which they were attempting to make a substituted diethietene 

complex of uranium. Other details of the sample preparation are not given. 

Because the disparate data sets were derived from samples having different 

synthesis histories, some support is given to the idea that a second monoclinic 

form of sulfur may exist in the narrow temperature interval of T = 368.3 to 374 

± 1 K. Final resolution of this dichotomy must await a more detailed structural 

analysis of sulfur in this region of temperature.

The average of the four values for the enthalpy of transition from 

orthorhombic to monoclinic sulfur, AtrsH° = (401.2 ± 1) J-mol"1 , is in good 

agreement with the results of West, (2> (401.7 ± 2) J-mol' 1 , and Montgomery, (3) 

(400.4 ± 2.9) J-mol' 1 . It should be noted here that if a second monoclinic form 

does exist, the procedure used in this study captures any enthalpic effect in the 

value reported for the enthalpy of the a-3 transition.

For completeness, we compare our results with those from five previous
experimental studies, and with three sets of earlier recommendations. Although 

measurements to be contrasted here were made on the basis of different 

temperature scales, adjustment of each set to ITS-90 would not bring about any 

significant difference in the Cp\ ms within the experimental uncertainties.

The standard molar entropy obtained in this study for orthorhombic sulfur 

at T = 298.15 K, (31.953 ± 0.083) J-K' 1 -mol' 1 , is in good agreement with the 

values recommended by CODATA, (19) (32.045 ± 0.050) J-K^-mol' 1 ; Gurvich et al. , (20) 

(32.070 ± 0.080) J-K^-mol' 1 ; and the JANAF Thermochemical Tables (32.056 ± 0.050) 

J-K^-mol" 1 . 121) The CODATA selection was calculated from the heat capacities 

reported by Berezovskii and Paukov(8) {5 <. (T/K) <. 306}, Eastman and McGavock(7) (15 

<; (T/K) <: 361}, and Montgomery'3 * (12.3 <. (T/K) <; 36l}; Gurvich et al. used the 

data of Berezovskii and Paukov and Montgomery; and the JANAF table is based on 

Montgomery's results alone. Measurements by Mal'tsev and Demidenko (22) were 

performed over the limited temperature interval between 53 K and 305 K and, 

therefore, were not used in these evaluations.

Figure 3 compares the smoothed values in table 3 with those obtained by 

previous authors for orthorhombic sulfur. Despite the large differences in 

impurity contents of the various samples, there is remarkable agreement among the 

different studies except at low temperatures and in the transition to fusion 

region. It is interesting that, with each study treated independently, the 

values of AJS,; at T = 298.15 K agree within the assigned uncertainties.

The recommended value of Cp <m (T ~ 6 K) from Berezovskii and Paukov is about 

2% larger than ours, which is assumed to be due to the influence of contaminants. 

These authors gave some details of the purity of their sample, prepared by a 

method devised by Kiseleva and Smykova. 123 ' It contained as major impurity mass 

fraction 5-10' 4 of Si which, arguably, came from the silica apparatus in which 

the sulfur was prepared. In that case, the corresponding mass fraction of SiO2 

impurity would be = 10' 3 . Berezovskii and Paukov made no mention of C, H, O, or 

N contaminants. It is not unlikely that their sample had a mass fraction of 

impurity that exceeded ours by almost three powers of ten.

The heat capacities reported here increasingly diverge from those reported 

by Montgomery' 3 ' and West (2) for orthorhombic sulfur in the temperature range from 

298.15 K to 368.3 K, and for the monoclinic phase as well. There is good accord 

between the results at T = 368.3 K for the monoclinic phase, but they also 

deviate with increasing temperature. The values of dC°_ m/dT from West are similar 

to those found in this study, but the C° ims lie about 1 per cent below those 

listed in table 3. The smoothed C° ims from Montgomery deviate from ours by 

several per cent at T = 388.36 K. Experimental heat capacities for the 

temperature interval 364 K to 370 K given by Montgomery are not shown, but are 

in good agreement, with respect to both value and dCp /m/dT, with the measurements 

reported here. At T > 370 K, the C° >m against T curve obtained by Montgomery 

becomes horizontal and then breaks sharply downward at T = 384 K. We attribute 

this to the rupture of the sample container in the calorimeter, to which 

Montgomery referred in his thesis.

We wish to thank our U.S. Geological Survey colleague Howard T. Evans, Jr. 

for providing the X-ray analyses of the sulfur sample. Thanks are also due to 

Dr. S. Susman and Professor S. C. Rowland for providing the pure sulfur.
8

REFERENCES

1. Murphy, T. J.; Clabaugh, W. S.; Gilchrist, R. J. Res. Natl. Bur. Stand. 

(U.S.) 1960, 64A, 355-358.

2. West, E.D. J. Am. Chem. Soc. 1959, 81, 29-37.

3. Montgomery, R.L., Ph.D. Dissertation, Oklahoma State University, 1975.

4. Good, W. D.; Lacina, J. L.; McCullough, J. P. J. Am. Chem. Soc. 1960, 82, 

5589-5591.

5. Susman, S./ Rowland, S. C.; Volin, K. J. J. Mater. Res. 1992, 7, 1526- 

1533.

6. O'Hare, P. A. G.; Susman, S.; Volin, K. J.; Rowland, S.C. J. Chem. 

Thermodynamics 1992, 24, 1009-1017.

7. Eastman, E.D.; McGavock, W.C. J. Am. Chem. Soc. 1937, 59, 145-151.

8. Berezovskii, G.A.; Paukov, I.E. Russ. J. Phys. Chem. 1978, 52, 1541-1542.

9. Robie, R.A.; Hemingway, B.S. U.S. Geol. Survey Bull. 755 1972.

10. Robie, R.A. Hydrothermal Experimental Techniques. Ulmer, G.C.; Barnes, 

H.L.; editors. Wiley: New York. 1987, pp. 389-422.

11. Robie, R.A.; Hemingway, B.S.; Wilson, W.H. J. Res. U.S. Geol. Survey 

1976, 4, 631-644.

12. Martin, D. L. Rev. Sci. Instrum. 1987, 58, 639-646.

13. Osborne, D. W.; Flotow, H. E.; Schreiner, F. Rev. Sci. Instrum. 1967, 38, 

159-168.

14. Currell, R. R.; Williams, A. J. Thermochimica Acta 1974, 9, 255-259.

15. Templeton, L. K. ; Templeton, D. H.; Zalkin, A. Inorg. Chem. 1976, 15, 1999- 

2001.

16. Burwell, J. T., Ill Z. Krist. 1937, 97, 123-124.

17. Taylor, A.; Rummery, T. E. J. Inorg. Nucl. Chem. 1978, 40, 1444-1446.

18. Pinkus, A. G./ Kirn, J. S.; McAtee, J. L., Jr.; Concilio, C. B. J. Am. Chem. 

Soc. 1959, 81, 2652-2654.

19. Cox, J. D.; Wagman, D. D.; Medvedev, V. A.: editors. CODATA Key Values for 

Thermodynamics. Hemisphere: Washington, D.C. 1989. Table 5.

20. Gurvich, L. V.; Veyts, I. V.; Alcock, C. B. Thermodynamic Properties of 

Individual Substances. Vol. 1. Hemisphere: New York. 1989.

21. Chase, M.W., Jr.; Davies, C.A.; Downey, J.R., Jr.; Frurip, D.J.; McDonald, 

R.A.; Syverud, A.N. JANAF Thermochemical Tables, Third Edition. J. Phys. 

Chem. Ref. Data 1985, 14.

22. Mal'tsev, A. K.; Demidenko, A. F. Tr. Mosk. Khim.-Tekhnol. Inst. 1967, 

(51), 136-139.

23. Kiseleva, E. N.; Smykova, N. Ya. Zh. Prikl. Khim. 1974, 47, 447-448.
Table 1. Experimental heat capacities of copper corrected for curvature 

{M = 63.546 g-mor1 ; p = 100.000 kPa; R = 8.31451 J-mol^KT/K T/K T/K

Series 1

58.13

61.88

66.30

70.92

76.13

81.34

86.55

91.71

96.81

101.86

106.86

111.82

116.73

121.62

126.49

131.33

136.13

140.93

145.73

150.50

155.25

159.99

164.70

169.43

174.16

178.89

183.62

188.34

193.06

197.78

202.53

207.30

212.09

216.91

221.77

226.72

231.75

236.86

242.01

247.19

252.38

257.58

262.77

267.96

273.15

278.34

283.52

288.68

293.84

298.98

304.12

309.23

314.34

319.44

0.9859

1.093

1.214

1.334

1.461

1.579

1.687

1.786

1.875

1.955

2.028

2.095

2.156

2.212

2.264

2.311

2.354

2.394

2.431

2.464

2.496

2.525

2.554

2.579

2.604

2.627

2.650

2.670

2.688

2.707

2.724

2.739

2.754

2.769

2.783

2.796

2.810

2.823

2.835

2.847

2.858

2.869

2.879

2.888

2.897

2.908

2.915

2.924

2.933

2.939

2.946

2.955

2.962

2.968

Series 2

56.86

60.66

65.06

69.67

74.89

80.12

85.32

90.48

95.58

100.61

105.60

110.55

115.45

120.30

125.13

129.95

134.73

139.49

144.24

148.98

153.71

158.42

163.11

167.78

172.45

177.12

181.81

186.48

191.16

195.85

200.54

205.25

209.99

214.76

219.57

224.44

229.42

234.50

239.65

244.83

250.03

255.23

260.43

265.62

270.81

276.00

281.19

286.35

291.51

296.66

301.80

306.92

312.04

317.14

0.9491

1.058

1.180

1.302

1.432

1.552

1.663

1.763

1.854

1.936

2.010

2.079

2.140

2.197

2.250

2.298

2.342

2.382

2.420

2.454

2.486

2.516

2.544

2.571

2.595

2.618

2.641

2.662

2.681

2.700

2.717

2.733

2.748

2.763

2.776

2.790

2.804

2.816

2.828

2.842

2.854

2.865

2.874

2.883

2.893

2.901

2.910

2.919

2.928

2.936

2.944

2.951

2.958

2.965

Series 3

5.863

6.761

7.981

8.267

Series 4

6.997

Series 5

6.633

8.023

9.627

12.25

Series 6

11.28

12.67

13.42

14.31

Series 7

13.09

13.80

14.93

15.71

16.69

17.86

19.24

20.85

22.70

24.81

27.20

29.88

32.90

36.30

40.10

44.31

49.00

54.29

59.85

65.42

71.01

76.49

81.88

87.15

92.32

97.44

102.46

107.42

112.34

117.22

122.07

0.001728

0.002303

0.003499

0.003992

0.002592

0.002223

0.003553

0.005876

0.01162

0.009105

0.01294

0.01549

0.01909

0.01437

0.01701

0.02185

0.02575

0.03108

0.03849

0.04896

0.06362

0.08388

0.1120

0.1501

0.2003

0.2655

0.3482

0.4506

0.5720

0.7128

0.8700

1.032

1.189

1.338

1.470

1.592

1.700

1.797

1.885

1.964

2.036

2.102

2.162

2.217
Table 2. Experimental heat capacities of orthorhombic sulfur corrected for 

curvature 

(M = 32.066 g-mor1 ; p = 100.000 kPa; R = 8.31451 J-mor'-K'1 }

T/K Cp> JR T/K Cpim/R T/K

Series 1

6.009

6.717

7.614

8.514

9.926

11.212

Series 2

6.635

7.263

8.015

9.084

9.874

11.022

12.096

13.274

Series 3

9.676

10.40

11.69

12.62

14.06

15.01

16.13

17.45

18.93

20.63

22.56

24.73

27.15

29.85

32.84

36.15

39.82

43.81

0.01859

0.02377

0.03217

0.04188

0.05964

0.08299

0.02322

0.02856

0.03620

0.04859

0.06149

0.07891

0.09977

0.1274

0.05775

0.06855

0.09127

0.1120

0.1471

0.1719

0.2015

0.2365

0.2765

0.3215

0.3706

0.4246

0.4818

0.5409

0.6018

0.6643

0.7307

0.8034

Series 3

48.20

53.16

58.45

63.90

69.40

74.83

80.16

85.40

90.61

95.78

100.88

105.94

110.96

115.89

120.77

125.60

130.40

135.16

139.89

144.58

149.25

153.89

158.50

163.09

167.66

172.22

176.76

181.29

185.81

190.32

194.82

199.33

203.83

208.34

212.85

217.38

221.92

226.52

0.8682

0.9349

1.004

1.087

1.177

1.250

1.315

1.370

1.434

1.489

1.553

1.595

1.643

1.692

1.739

1.786

1.829

1.870

1.910

1.948

1.984

2.021

2.055

2.089

2.123

2.155

2.185

2.214

2.244

2.272

2.298

2.322

2.347

2.369

2.392

2.413

2.436

2.456

Series 3

231.18

235.89

240.65

245.43

250.23

255.04

259.85

264.70

269.58

274.46

279.32

284.17

289.03

293.83

298.64

Series 4

294.63

299.23

303.87

308.50

313.22

317.93

322.63

327.31

331.98

336.65

341.30

345.96

350.64

355.31

359.97

364.61

Series 5

364.66

2.478

2.499

2.522

2.543

2.563

2.582

2.600

2.617

2.635

2.651

2.665

2.683

2.704

2.721

2.733

2.717

2.734

2.748

2.761

2.777

2.789

2.800

2.811

2.824

2.838

2.849

2.865

2.879

2.890

2.900

2.909

2.910
Table 3. Standard molar thermodynamic properties of reference state sulfur 

{M = 32.066 g-mor1 ; p = 100.000 kPa; R = 8.31451 J-mol^K'; &m =

T Cp>m A0X &lHm/T 0m

K

5

10

15

20

25

30

35

40

45

50

60

70

80

90

100

110

120

130

140

150

160

170

180

190

200

210

220

230

240

250

260

270

273.15

280

290

298.15

300

310

320

330

340

350

360

365

368.3

368.3

370

380

388.36

R

0.0078

0.062

0.172

0.304

0.431

0.544

0.644

0.735

0.818

0.892

1.033

1.179

1.311

1.428

1.536

1.636

1.732

1.825

1.911

1.990

2.067

2.140

2.207

2.270

2.326

2.378

2.426

2.473

2.518

2.562

2.600

2.636

2.647

2.670

2.705

2.730

+0.008

2.736

2.766

2.794

2.820

2.848

2.874

2.900

2.915

2.924

2.984

2.991

3.034

3.069

R

0.0025

0.0207

0.0646

0.1321

0.2137

0.3025

0.3939

0.4859

0.5774

0.6675

0.8425

1.013

1.179

1.340

1.496

1.648

1.794

1.936

2.075

2.209

2.340

2.468

2.592

2.713

2.831

2.945

3.057

3.167

3.273

3.376

3.477

3.577

3.610

3.673

3.767

3.843

+0.010

3.860

3.950

4.038

4.124

4.208

4.291

4.373

4.414

4.439

4.570

4.585

4.665

4.731

*-K

0.0017

0.0091

0.0434

0.0919

0.1472

0.2041

0.2599

0.3137

0.3651

0.4142

0.5056

0.5914

0.6734

0.7507

0.8240

0.8933

0.9593

1.022

1.083

1.141

1.196

1.250

1.301

1.351

1.398

1.443

1.487

1.529

1.568

1.608

1.645

1.681

1.692

1.716

1.750

1.776

+0.005

1.781

1.812

1.844

1.873

1.900

1.928

1.954

1.968

1.976

2.107

2.111

2.135

2.155

R

0.0008

0.0116

0.0212

0.0402

0.0665

0.0984

0.1340

0.1722

0.2123

0.2533

0.3369

0.4216

0.5056

0.5893

0.6720

0.7547

0.8347

0.9137

0.9923

1.068

1.144

1.218

1.291

1.362

1.433

1.502

1.570

1.638

1.705

1.768

1.832

1.896

1.918

1.957

2.017

2.067

+ 0.010

2.079

2.138

2.194

2.251

2.308

2.363

2.419

2.445

2.463

2.463

2.474

2.530

2.576
Table 4. Experimental heat capacities 

of monoclinic sulfur corrected for 

curvature {M = 32.066 g-mol"1 ; 

p = 100.000 kPa; 

R = 8.31451

r/K cp>m/R

Series 1

382.25

383.84

Series 2

373.19

374.30

375.77

377.76

380.19

Series 3

380.20

381.30

382.88

384.73

386.02

386.83

Series 4

368.58

369.71

371.19

372.77

374.36

375.94

Series 5

368.26

371.10

373.49

375.89

378.75

382.03

385.30

3.044

3.051

3.011

3.012

3.019

3.025

3.033

3.033

3.037

3.044

3.058

3.071

3.090

2.986

2.990

2.998

2.998

3.006

3.015

2.992

2.998

3.006

3.018

3.028

3.042

3.058
Table 5. Enthalpy of the transformation, A#p m , of orthorhombic to

monoclinic sulfur at 368.3 K {M = 32.066 g-mol"1 ; 

p = 100.000 kPa}

Sample mass Initial Final Energy Enthalpy

Temperature of Transition

g 77K 7VK J-mol'1

29.4592 363.554 376.588 724.45 402.5

29.4592 366.661 381.774 777.82 400.6

27.3389 366.014 381.126 777.10 400.5

27.2366 366.594 375.633 625.68 401.3

Average value 401.3

±0.8

West (1959) 401.7

±2.0

Montgomery (1975) 400.5
List of Figures

Figure 1. Deviation of the experimental heat-capacity values from the 

smoothed heat-capacities.

Figure 2. Smoothed heat capacities for equilibrium sulfur. The a-3 and 

melting point transitions are 368.3 and 388.36 K, respectively.

Figure 3.Comparison of the smoothed values for the heat capacity of

sulfur reported in this study (solid line) with those reported by 

Montgomery (3) (dash dot curve) , West 121 (dashed curve) , Eastman and 

McGavock 17 ' (dot curve) , and Berezovskii and Paukov (8) (long dash 

short dash curve).
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