^-t ^ :<;^J/A on^ -/^f^ MDDC - 1096 UNITED STATES ATOMIC ENERGY COMMISSION SPECIFIC HEAT, ENTHALPY, AND ENTROPY OF URANYL FLUORIDE by Paul F. Wacker Ruth K. Cheney National Bureau of Standards . ENGINHITRrVO UNIV. OF FL LIB jOCUMENT- ; r)FP-[ U.S. DEPOSITORY This document consists of 5 pages. Date of Manuscript: Unknown Date Declassified: July 9, 1947 This document is issued for official use. Its issuance does not constitute authority to declassify copies or versions of the same or similar content and title and by the same author(s). Technical Information Division, Oak Ridge Directed Operations Oak Ridge, Tennessee SPECIFIC HEAT, ENTHALPY, AND ENTROPY OF URANYL FLUORIDE By Paul F. Wacker and Ruth K. Cheney ABSTRACT The heat capacity of uranyl fluoride was measured from 13° to 418°K using a vacuum-type calorimeter equipped with thermostated radiation shields. From the data so obtained, the enthalpy H° - H° was calculated to be 63.96, 77.62, and 108.15 int. joules per gram at 298.16, 338.16, and 423.16°K respectively, while the entropy was calculated to be 0.4400, 0.4830, and 0.5635 int joules per degree-gram at the same temperatures. No evidence of a transition was found. The values of the specific heat, enthalpy, entropy, and free energy are tabulated at five degree intervals of temperature. INTRODUCTION This investigation of the thermodynamic properties of uranyl fluoride was undertaken in connec- tion with the Manhattan project and is a part of the program carried on during the war by the Heat and Power Division of the National Bureau of Standards. MATERIAL The uranyl fluoride used in this investigation was prepared by H. F. Priest of Columbia University. The material was placed in the sample container after being dried at 130°C for four hours. Air was removed by pumping until a high vacuum was obtained, helium was admitted at a pressure of 20 mm Hg, and the container was sealed with solder. The helium was added to promote the rapid attainment of thermal equilibrium. The observed heat capacity was adjusted for the presence of this helium. Before the material was used in the calorimeter, an analysis made by the SAM Laboratories of the Carbide and Carbon Chemicals Corporation showed the sample to contain 77.19 weight per cent of uranium and 12.64 weight per cent of fluorine. Following the calorimetric measurements, the Uranium Section of the National Bureau of Standards found the sample to contain 77.28 per cent of uranium and 12.1 per cent of fluorine. The theoretical percentages are 77.28 and 12.33. Spectroscopic, tests for 34 elements showed less than 0.07 weight per cent impurity. The difficulties in fluorine anal- ysis are such that it is probably improper to base any conclusions regarding purity of the sample on observed fluorine content. APPARATUS AND PROCEDURE The calorimeter used in this investigation was of the adiabatic, vacuum type described by Southard and Brickwedde.' The sample container was the one used in the determination of the heat capacities of GR-S rubber^ and polyvinyl chloride.' The system, including tlie measuring circuits, was very similar to that used by Scott, Meyers, Rands, Brickwedde, and Bekkedahl'' to determine the heat capaciiy of butadiene, except for the follow- ing: The apparatus was designed for measuring the heat capacitie.~. of solids and so had no filling tube or attendant parts. The shield was suspended by means of fine wire, and the sample container was in turn suspended from the shield by means of linen cord. A copper, rather than an aluminum, shield was used on the bottom of the sample container to prevent heat losses from the exposed ends of the heater. The sample -container heater was located in the thermometer well, which was filled with lead-tin eutectic solder. The side and bottom shield heaters were controlled individually. In order to improve MDDC - 1096 [ 1 MDDC - 1096 the ease of controlling the radiation shields at temperatures above the ice point, an auxiliary heater was wrapped on the outer wall of the vacuum chamber, and the chamber was surrounded by a stirred oil bath. The auxiliary heater was used to keep this wall at a temperature only slightly below that of the shields and sample container. Its use resulted in a substantial improvement in shield control. Temperatures were measured with platinum resistance thermometer L15 (thermometer P), whose calibration is described by Hege and Brickwedde.^ The methods of measurement and of calculation were similar to those described in the paper on butadiene.'' The tare heat capacity measurements were made on the empty sample container, while the gross heat capacity measurements were made with 58.015 grams of uranyl fluoride in the con- tainer. Due to the negligible vapor pressure of the material, it was unnecessary to correct the heat capacities for vaporization. Specific heat measurements were regularly made with both high and low heating rates, the rates varying as much as from 0.63 to 2.18 degrees per minute. This procedure provided a test for a large proportion of the errors which might occur in the measurement of heat capacity, but would not have revealed an error whose magnitude per unit time was proportional to the heating rate. CALCULATIONS AND RESULTS The observed heat capacity data were plotted as deviations from empirical equations. From the resulting deviation curves, values were read at uniform temperature intervals, and tables were con- structed giving both the gross and tare heat capacities at 2.5-degree intervals below 115°K and at 5-degree intervals at higher temperatures. Subtraction of the tare from the gross heat capacity gave the net heat capacity, which was extrapolated to 0°K by means of the Debye equation, C = 0.8359 D(117/T). This equation represented the experimental data satisfactorily at 20, 25, and 30°K. Due to graphical methods involved in getting the table of net heat capacities, small irregularities could be detected in the higher differences. To reduce these, an analytical smoothing process was applied. The smoothed value corresponding to a given unsmoothed value was found by multiplying the unsmoothed value and the four adjacent unsmoothed values on either side of it by a set of coefficients. A number of such smoothing processes have been devised. The one adopted in the present work was developed by Harold W. Wooley. In it the coefficients were chosen to minimize the squares of the random parts of the first differences in such a manner that the process would make no significant change in functions for which the fourth and higher differences were negligible. The smoothing oper- ation introduced no changes in the table as large as the probable experimental error. The enthalpy was calculated from the formlua H° = f C AT, while the entropy was obtained from the equation S° = fiC'/T) dT. The free energy was calculated from the relation F° = -/s° dT and also from the relation F° = H° - TS°. This provided a check on the accuracy of the integrations. Simpson's rule was used at the higher temperatures. Between 20° and 115°K, a tabular integration formula involving four rather than three successive tabular entries was used, while below 20° the inte- grals were obtained directly from the Debye equation. The results are presented in Table 1. The dashed lines in Figure 1, representing 1/2 per cent of the heqt capacity, show the temperature trend of the specific heat. DISCUSSION Although tests were made for transitions, none were found. The probable error in the tabulated values of the specific heat of the sample used in this investi- gation is estimated to be 0.1 per cent from 40 to 250°K. Below 40° the error is larger, perhaps reach- ing 1 per cent at 20°K. Since radiation becomes an important source of error above room temperature, the probable error above 250'K may be as large as 0.5 per cent. These estimates do not include errors due to impurities in the sample. Although there is probably no reliable evidence for more than 0.07 weight per cent impurity in the sample, the lack of detailed knowledge of the purity does introduce some uncertainty in the results. MDDC - 1096 3] Table 1. Heat capacity, enthalpy, entropy, and free energy of uranyl fluoride. T C° H'-H° S° -(F^-H^) T C h°-h: S° -(F°-H°) °K Int.jg-"K-' Int.jg-' Int.jg-' "K"' Int.jg-' °K Int.jg-' °K-' Int.jg-' Int.jg-' °K-' Int.jg-' 0. 0. 0. 0. 215 .2949 37.626 .33687 34.802 5 .00051 .00064 .00017 .00021 220 .2979 39.107 .34368 36.503 10 .00403 .01014 .00135 .00339 225 .3008 40.604 .35041 38.238 15 .01231 .0492 .00440 .01690 230 .3037 42.116 .35705 40.006 20 .02333 .1378 .00943 .0508 235 .3064 43.641 .36361 41.808 25 .03386 .2803 .01575 .1133 240 .3090 45.179 .37009 43.643 30 .04478 .4768 .02288 .2096 245 .3116 46.731 .37649 45.510 35 .05567 .7280 .03060 .3431 250 .3142 48.295 .38281 47.408 40 .06637 1.0331 .03874 .5163 255 .3166 49.872 .38905 49.337 45 .07747 1.3925 .04719 .7310 260 .3190 51.462 .39523 51.298 50 .08909 1.8086 .05595 .9887 265 .3214 53.063 .40133 53.290 55 .10191 2.2855 .06503 1.2910 270 .3237 54.676 .40735 55.310 60 .11549 2.8292 .07448 1.6396 275 .3259 56.300 .41331 57.362 65 .12713 3.4371 .08420 2.0363 280 .3280 57.934 .41920 ■ 59.443 70. .13573 4.0951 .09395 2.4817 285 .3300 59.579 .42503 61.555 75 .14362 4.7933 .10358 2.9756 290 .3320 61.235 .43079 63.694 80 .15261 5.5333 .11313 3.5174 295 .3339 62.900 .43648 65.862 85 .16310 6.3220 .12269 4.1070 300 .3357 64.574 .44210 68.058 90 .17378 7.1647 .13232 4.7443 305 .3374 66.256 .44767 70.284 95 .18226 8.0560 .14196 5.4302 310 .3390 67.947 .45317 72.536 100 .18847 8.9834 .15147 6.1638 315 .3406 69.647 .45860 74.814 105 .19439 9.9404 .16081 6.9446 320 ' .3422 71.354 .46398 77.121 110 .2007 10.928 .16999 7.7713 325 .3438 73.069 .46930 79.454 115 .2070 11.947 .17905 8.6440 330 .3454 74.792 .47456 81.814 120 .2132 12.998 .18800 9.5620 335 .3470 76.523 .47976 84.199 125 .2193 14.079 .19682 10.524 340 .3486 78.262 .48492 86.612 130 .2252 15.190 .20554 11.530 345 .3502 80.009 ^49002 89.049 135 .2308 16.331 .21415 12.579 350 .3517 81.764 .49507 91.512 140 .2362 17.498 .22264 13.671 355 .3532 83.526 .50007 94.000 145 .2413 18.692 .23102 14.806 360 .3546 85.296 .50502 96.512 ipo. .2463 19.911 .23928 15.981 365 .3560 87.072 .50992 99.050 155 .2510 21.154 .24743 17.198 370 .3572 88.855 .51477 101.611 160 .2556 22.421 .25547 18.455 375 .3584 90.645 .51957 104.196 165 .2598 23.710 .26340 19.752 380 .3596 92.440 .52433 106.806 170 .2640 25.019 .27122 21.089 385 .3607 94.241 .52904 109.440 175 .2679 26.349 .27893 22.464 390 .3617 96.046 .53370 112.098 180 .2717 27.698 .28653 23.878 395 .3627 97.858 .53831 114.776 185 .2753 .2788 29.066 .29403 25.330 26.818 400 405 .3638 .3648 99.674 101.495 .54288 .54741 117.480 190 30.451 .30141 120.206 195 .2822 31.854 .30870 28.343 410 .3658 103.321 .55189 122.954 200 .2854 33.273 .31589 29.906 415 .3668 105.153 .55633 125.725 205 .2886 34.708 .32297 31.502 420 .3678 106.989 .56073 128.518 210 .2917 36.159 .32997 33.135 425 .3688 108.831 .56508 131.330 'C I:." 41 MDDC - 1096 "Ao ,-6( '(D|DO-sqo) 6f'(3|D0-sqo) OV MDDC - 1096 REFERENCES 1. 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