THERMODYNAMIC PROPERTIES OF COPPER
SUPPLEMENTARY INFORMATION
J.W.Arblaster
DATA USED IN THE EVALUATION
A. SOLID : TEMPERATURE RANGE 0 TO 30 K
Select γ = 0.694 J∙mol-1∙K-2 ; ΘD = 344.3 K Fit to Equation (1)
Cºp (J∙mol-1∙K-1) = 6.94000 x 10-4 T + 4.76249 x 10-5 T 3 + 1.05866 x 10-9 T 5 + 1.02870 x 10-10 T 7
– 1.68191 x 10-13 T 9 + 9.01270 x 10-17 T 11 – 1.13003 x 10-20 T 13
± 0.0006 J∙mol-1∙K-1 (0.20%)
A1. Ahlers 1966 [38]
1.3 to 20 K. No atomic weight value given
Cºp (mJ∙mol-1∙K-1) = 0.69597 T + 4.7828 x 10-2 T 3 – 1.2613 x 10-5 T 5 + 2.1747 x 10-7 T 7
– 4.9552 x 10-10 T 9 + 3.9236 x 10-13 T 11
A2. Osborne et al 1967 [40]
1.03 to 22.57 K. 37 data points fitted by Hurley and Gernstein 1974 [59]. No atomic weight value given
Cºp (mJ∙mol-1∙K-1) = 0.69366 T + 4.7254 x 10-2 T 3 + 2.2340 x 10-5 T 5 – 2.1396 x 10-7 T 7
+ 1.7871 x 10-9 T 9 – 5.7007 x 10-12 T 11+ 8.0979 x 10-15 T 13 – 4.28073 x 10-18 T 15
A3. Holste et al 1972 [55]
TX scale 1 to 30 K. No atomic weight value given. Vacuum annealed sample
Cºp (mJ∙mol-1∙K-1) = 0.69260 T + 4.7369 x 10-2 T 3 + 1.9537 x 10-6 T 5 + 1.0869 x 10-7 T 7
– 1.9745 x 10-10 T 9 + 1.3343 x 10-13 T 11 – 3.2196 x 10-17 T 13
A4. Martin et al 1973 [56]
3 to 30 K. Atomic weight 63.54. Includes Martin 1968, 1969
Cºp (mcal∙mol-1∙K-1) = 0.16508 T + 1.1372 x 10-2 T 3 + 2.4575 x 10-7 T 5 + 2.4577 x 10-8 T 7
– 4.0003 x 10-11 T 9 + 2.0914 x 10-14 T 11 – 2.2097 x 10-18 T 13
A5. Martin 1973 [58]
2.5 to 30 K. Atomic weight 63.54.
Cºp (mcal∙mol-1∙K-1) = 0.16499 T + 1.1381 x 10-2 T 3 + 7.3330 x 10-8 T 5 + 2.5735 x 10-8 T 7
– 4.3285 x 10-11 T 9 + 2.4999 x 10-14 T 11 – 4.0511 x 10-18 T 13
A6. Hurley and Gerstein 1974 [59]
0.63 to 27.85 K
Cºp (mJ∙mol-1∙K-1) = 0.69142 T + 4.7807 x 10-2 T 3 + 2.9721 x 10-6 T 5 + 8.9189 x 10-8 T 7
– 1.3563 x 10-10 T 9 + 5.7469 x 10-14 T 11
Equal table – Cp units mJ∙mol-1∙K-1
A1 / A2 / A3 / A4 / A5 / A6T K / CP / T K / CP / T K / CP / T K / CP / T K / CP / T K / CP
5.0
5.6
6.2
6.8
7.4
8.0
8.6
9.2
9.8
10.4
11.0
11.6
12.2
12.8
13.4
14.0
14.6
15.2
15.8
16.4
17.0
17.6
18.2
18.8
19.4
20.0 / 9.4350
12.262
15.668
19.719
24.484
30.035
36.450
43.810
52.202
61.720
72.465
84.541
98.061
113.14
129.91
148.48
168.98
191.54
216.29
243.34
272.82
304.86
339.57
377.09
417.57
461.19 / 5.00
5.68
6.36
7.04
7.72
8.40
9.08
9.76
10.44
10.12
11.80
12.48
13.16
13.84
14.52
15.20
15.88
16.56
17.24
17.92
18.60
19.28
19.96
20.64
21.32
22.00 / 9.4314
12.700
16.737
21.639
27.503
34.434
42.538
51.932
62.741
75.104
89.171
105.11
123.10
143.33
166.00
191.30
219.43
250.56
284.86
322.49
363.62
408.42
457.13
510.09
567.72
630.57 / 5
6
7
8
9
10
11
12
13
14
15
16
17
18
19
20
21
22
23
24
25
26
27
28
29
30 / 9.3983
14.431
21.210
30.060
41.328
55.393
72.671
93.622
118.75
148.62
183.81
224.96
272.71
327.70
390.53
461.77
541.90
631.29
730.18
838.71
956.86
1084.6
1221.6
1368.0
1523.5
1688.3 / 5
6
7
8
9
10
11
12
13
14
15
16
17
18
19
20
21
22
23
24
25
26
27
28
29
30 / 9.4165
14.464
21.260
30.129
41.413
55.486
72.761
93.693
118.78
148.58
183.69
224.73
272.35
327.21
389.92
461.06
541.09
630.68
729.13
837.43
955.21
1082.4
1218.8
1364.7
1520.7
1688.4 / 5
6
7
8
9
10
11
12
13
14
15
16
17
18
19
20
21
22
23
24
25
26
27
28
29
30 / 9.4174
14.465
21.262
30.130
41.412
55.484
72.758
93.689
118.78
148.58
183.69
224.77
272.37
327.24
389.95
461.08
541.10
630.67
729.11
837.46
955.20
1082.4
1218.9
1364.9
1520.7
1687.5 / 5.00
5.88
6.76
7.64
8.52
9.40
10.28
11.16
12.04
12.92
13.80
14.68
15.56
16.44
17.32
18.20
19.08
19.96
20.84
21.72
22.60
23.48
24.36
25.24
26.12
27.00 / 9.4490
13.826
19.538
28.803
35.851
46.292
60.301
76.257
95.110
117.20
142.91
172.62
206.76
245.77
290.09
340.18
396.44
459.27
529.00
605.89
690.11
781.73
880.73
986.80
1100.3
1220.5
B. SOLID : TEMPERATURE RANGE 30 TO 400 K
B1. Robie et al 1976 [66]
Cp data in J∙mol-1∙K-1. Original temperature scale IPTS-68 (T68) and revised temperature scale ITS-90 (T90)
T68 K / 15.36 / 17.39 / 19.52 / 21.70 / 24.25 / 26.95 / 29.58 / 32.51 / 35.94 / 39.77 / 44.02T90 K / 15.36 / 17.38 / 19.51 / 21.69 / 24.24 / 26.95 / 29.57 / 32.50 / 35.93 / 39.76 / 44.01
Cp / 0.1981 / 0.2995 / 0.4221 / 0.5995 / 0.8632 / 1.210 / 1.610 / 2.133 / 2.824 / 3.671 / 4.680
T68 K / 48.38 / 56.68 / 59.10 / 62.65 / 64.41 / 67.82 / 69.47 / 73.04 / 74.71 / 78.39 / 80.17
T90 K / 48.37 / 56.68 / 59.10 / 62.65 / 64.42 / 67.83 / 69.48 / 73.05 / 74.72 / 78.70 / 80.18
Cp / 5.764 / 7.851 / 8.452 / 9.273 / 9.683 / 10.43 / 10.81 / 11.54 / 11.90 / 12.59 / 12.90
T68 K / 83.87 / 87.08 / 92.57 / 100.23 / 109.86 / 117.81 / 118.90 / 122.33 / 127.33 / 127.52 / 132.42
T90 K / 83.88 / 87.09 / 92.58 / 100.24 / 109.87 / 117.82 / 118.91 / 122.34 / 127.34 / 127.53 / 132.43
Cp / 13.59 / 14.13 / 14.99 / 16.06 / 17.22 / 18.04 / 18.15 / 18.47 / 18.92 / 18.92 / 19.30
T68 K / 135.81 / 137.54 / 142.97 / 143.76 / 151.22 / 151.88 / 158.67 / 166.21 / 173.63 / 180.94 / 186.21
T90 K / 135.82 / 137.55 / 142.97 / 143.77 / 151.23 / 151.89 / 158.68 / 166.22 / 173.63 / 180.94 / 186.22
Cp / 19.56 / 19.68 / 20.05 / 20.09 / 20.53 / 20.58 / 20.94 / 21.30 / 21.63 / 21.93 / 22.11
T68 K / 193.43 / 200.50 / 206.97 / 207.50 / 213.90 / 221.23 / 228.93 / 236.55 / 237.82 / 245.47 / 253.00
T90 K / 193.44 / 200.51 / 206.97 / 207.51 / 213.91 / 221.24 / 228.93 / 236.56 / 237.83 / 245.48 / 253.00
Cp / 22.36 / 22.58 / 22.76 / 22.78 / 22.94 / 23.12 / 23.30 / 23.47 / 23.44 / 23.63 / 23.79
T68 K / 260.68 / 268.12 / 275.53 / 282.89 / 290.22 / 295.34 / 297.53 / 302.69 / 305.90 / 306.40 / 306.65
T90 K / 260.68 / 268.12 / 275.53 / 282.89 / 290.22 / 295.34 / 297.52 / 302.68 / 305.89 / 306.39 / 306.64
Cp / 23.88 / 24.01 / 24.13 / 24.24 / 24.36 / 24.41 / 24.43 / 24.50 / 24.53 / 24.54 / 24.54
T68 K / 309.92 / 312.54 / 313.11 / 319.91 / 326.56 / 333.14 / 339.71 / 346.24 / 352.76 / 359.47 / 366.13
T90 K / 309.91 / 312.53 / 313.10 / 319.90 / 326.55 / 333.12 / 339.69 / 346.22 / 352.74 / 359.45 / 366.11
Cp / 24.58 / 24.61 / 24.61 / 24.68 / 24.76 / 24.84 / 24.89 / 24.96 / 25.02 / 25.08 / 25.15
T68 K / 372.70 / 379.26
T90 K / 372.67 / 379.23
Cp / 25.20 / 25.25
B2. Martin 1987 [67]
Original give as equation of Cp in J∙mol-1∙K-1 on IPTS-68 over range 20 to 320 K. Equation corrected to ITS-90 by Archer 1997 [71] :
Cp = – 0.8209550462989 – 0.1877080114403 T – 1.572088570716 x 10-2 T 2
+ 5.832484862761 x 10-4 T 3 – 1.452296533129 x 10-6 T 4 – 3.457773461093 x 10-7 T 5
+ 1.029537684534 x 10-8 T 6 – 1.620547240203 x 10-10 T 7 + 1.677835991722 x 10-12 T 8
– 1.225710530439 x 10-14 T 9 + 6.497060325945 x 10-17 T 10 – 2.516789895111 x 10-19 T 11
+ 7.064523085264 x 10-22 T 12 – 1.400131357648 x 10-24 T 13 + 1.858718557094 x 10-27 T 14
– 1.483505970215 x 10-30 T 15 + 5.382629833814 x 10-34 T 16
T K / 32 / 34 / 36 / 38 / 40 / 42 / 44 / 46 / 48 / 50Cp 90 / 2.039 / 2.423 / 2.835 / 3.270 / 3.725 / 4.195 / 4.679 / 5.171 / 5.669 / 6.169
T K / 52 / 54 / 55 / 56 / 58 / 61 / 64 / 67 / 70 / 72
Cp 90 / 6.670 / 7.169 / 7.417 / 7.663 / 8.152 / 8.871 / 9.569 / 10.245 / 10.896 / 11.315
T K / 73 / 76 / 79 / 80 / 84 / 88 / 92 / 96 / 100 / 104
Cp 90 / 11.520 / 12.119 / 12.692 / 12.877 / 13.588 / 14.256 / 14.881 / 15.466 / 16.013 / 16.523
T K / 105 / 108 / 110 / 112 / 115 / 116 / 120 / 125 / 130 / 135
Cp 90 / 16.645 / 16.999 / 17.225 / 17.443 / 17.757 / 17.857 / 18.244 / 18.692 / 19.103 / 19.483
T K / 140 / 145 / 150 / 155 / 160 / 165 / 170 / 175 / 180 / 185
Cp 90 / 19.834 / 20.160 / 20.462 / 20.744 / 21.006 / 21.250 / 21.478 / 21.690 / 21.888 / 22.073
T K / 190 / 195 / 200 / 205 / 208 / 210 / 211 / 214 / 215 / 217
Cp 90 / 22.246 / 22.408 / 22.561 / 22.706 / 22.789 / 22.844 / 22.870 / 22.949 / 22.975 / 23.025
T K / 220 / 223 / 226 / 229 / 232 / 235 / 238 / 241 / 244 / 247
Cp 90 / 23.099 / 23.171 / 23.240 / 23.308 / 23.373 / 23.435 / 23.496 / 23.554 / 23.611 / 23.666
T K / 250 / 253 / 256 / 259 / 262 / 265 / 268 / 271 / 273.15 / 274
Cp 90 / 23.718 / 23.770 / 23.820 / 23.869 / 23.917 / 23.965 / 24.011 / 24.058 / 24.102
T K / 277 / 280 / 283 / 286 / 289 / 292 / 295 / 298.15 / 301 / 304
Cp 90 / 24.147 / 24.192 / 24.235 / 24.278 / 24.330 / 24.360 / 24.398 / 24.435 / 24.471 / 24.505
T K / 307 / 310 / 313 / 316 / 319
Cp 90 / 24.538 / 24.570 / 24.602 / 24.636 / 24.672
B3. Stevens and Boerio-Goates 2004 [68]
Values of Cp in J∙mol-1∙K-1 given on ITS-90. Values at 12.43 K, 14.81 K and 378.00 K rejected
T K / 6.56 / 7.16 / 7.85 / 8.64 / 9.55 / 10.51 / 11.42 / 12.43 / 13.56 / 14.81 / 16.17Cp / 0.0232 / 0.0255 / 0.0323 / 0.0400 / 0.0534 / 0.0663 / 0.0839 / 0.1121 / 0.1370 / 0.1926 / 0.2314
T K / 17.69 / 19.34 / 20.19 / 21.13 / 21.94 / 23.08 / 23.76 / 25.79 / 28.01 / 30.46 / 33.17
Cp / 0.3040 / 0.4106 / 0.4727 / 0.5555 / 0.6242 / 0.7448 / 0.8181 / 1.0579 / 1.3702 / 1.7612 / 2.2593
T K / 36.05 / 37.57 / 39.01 / 40.74 / 44.10 / 45.89 / 47.52 / 49.38 / 52.99 / 54.47 / 56.65
Cp / 2.8525 / 3.1732 / 3.4970 / 3.8984 / 4.7081 / 5.1458 / 5.5489 / 6.0253 / 6.9332 / 7.2807 / 7.8371
T K / 56.87 / 59.76 / 62.64 / 66.47 / 71.22 / 75.97 / 80.79 / 85.65 / 90.55 / 95.49 / 100.46
Cp / 7.8818 / 8.5815 / 9.2716 / 10.136 / 11.164 / 12.131 / 13.040 / 13.887 / 14.676 / 15.408 / 16.084
T K / 105.45 / 110.46 / 115.49 / 120.54 / 125.61 / 130.68 / 134.74 / 135.77 / 139.84 / 140.87 / 144.94
Cp / 16.706 / 17.282 / 17.810 / 18.295 / 18.746 / 19.157 / 19.466 / 19.542 / 19.823 / 19.889 / 20.156
T K / 150.05 / 155.17 / 160.30 / 165.43 / 170.57 / 175.70 / 180.85 / 186.00 / 191.15 / 193.33 / 196.30
Cp / 20.465 / 20.750 / 21.019 / 21.267 / 21.500 / 21.718 / 21.920 / 22.107 / 22.281 / 22.353 / 22.446
T K / 198.48 / 201.46 / 203.64 / 206.62 / 208.80 / 213.96 / 219.13 / 224.29 / 229.45 / 232.56 / 234.62
Cp / 22.512 / 22.598 / 22.656 / 22.739 / 22.789 / 22.928 / 23.064 / 23.194 / 23.309 / 23.380 / 23.411
T K / 237.73 / 239.79 / 242.89 / 248.06 / 253.24 / 258.41 / 263.59 / 268.77 / 273.95 / 279.13 / 284.31
Cp / 23.486 / 23.527 / 23.592 / 23.683 / 23.766 / 23.858 / 23.951 / 24.024 / 24.089 / 24.160 / 24.234
T K / 289.49 / 294.67 / 297.38 / 299.85 / 302.55 / 307.73 / 312.92 / 318.10 / 323.28 / 325.89 / 328.47
Cp / 24.307 / 24.377 / 24.412 / 24.444 / 24.489 / 24.553 / 24.612 / 24.674 / 24.726 / 24.750 / 24.782
T K / 331.06 / 336.25 / 341.44 / 346.62 / 351.80 / 356.99 / 363.06 / 368.04 / 373.02 / 378.00 / 382.98
Cp / 24.795 / 24.853 / 24.911 / 24.947 / 24.992 / 25.031 / 25.066 / 25.115 / 25.171 / 25.254 / 25.247
T K / 387.96 / 392.94 / 397.62
Cp / 25.302 / 25.351 / 25.408
B4. Bissengaliyeva et al 2011 [69]
Cp values in J∙mol-1∙K-1 given on ITS-90 evaluated from equations :
4.2 to 5.5 K : Cp = – 0.065005 + 0.0421651 T – 8.7718 x 10-3 T 2 – 6.6299 x 10-4 T 3
5.5 to 8 K : Cp = 0.048611 – 0.0208889 T + 3.1556 x 10-3 T 2 – 1.0419 x 10-4 T 3
8 to 13 K : Cp = 0.022531 – 0.0050360 T + 4.1684 x 10-4 T 2 + 4.1349 x 10-5 T 3
13 to 20 K : Cp = – 0.131088 + 0.0303737 T – 2.3826 x 10-3 T 2 + 1.1720 x 10-4 T 3
20 to 30 K : Cp = 0.968573 – 0.1266262 T + 5.1522 x 10-3 T 2 – 4.5447 x 10-6 T 3
30 to 50 K : Cp = 2.203518 – 0.2684105 T + 1.0491 x 10-2 T 2 – 7.0706 x 10-5 T 3
50 to 80 K : Cp = – 5.902888 + 0.1933105 T + 1.7042 x 10-3 T 2 – 1.4804 x 10-5 T 3
80 to 120 K : Cp = –14.42312 + 0.5358163 T – 2.8991 x 10-3 T 2 + 5.8601 x 10-6 T 3
120 to 170 K : Cp = – 9.251221 + 0.4124027 T – 1.9199 x 10-3 T 2 + 3.2788 x 10-6 T 3
170 to 220 K : Cp = 2.781384 – 0.2001573 T – 6.6799 x 10-4 T 2 + 8.0924 x 10-7 T 3
220 to 270 K : Cp = 18.18368 + 0.0085765 T + 1.2289 x 10-4 T 2 – 2.7389 x 10-7 T 3
270 to 320 K : Cp = 33.52463 – 0.1302450 T + 5.2397 x 10-4 T 2 – 6.3449 x 10-7 T 3
T K / 32 / 34 / 36 / 38 / 40 / 42 / 44 / 46 / 48 / 50Cp / 2.040 / 2.426 / 2.828 / 3.273 / 3.728 / 4.198 / 4.681 / 5.172 / 5.672 / 6.173
T K / 52 / 54 / 55 / 56 / 58 / 61 / 64 / 67 / 70 / 72
Cp / 6.676 / 7.174 / 7.421 / 7.667 / 8.154 / 8.870 / 9.569 / 10.247 / 10.902 / 11.324
T K / 73 / 76 / 79 / 80 / 84 / 88 / 92 / 96 / 100 / 104
Cp / 11.531 / 12.134 / 12.706 / 12.889 / 13.603 / 14.272 / 14.897 / 15.482 / 16.028 / 16.537
T K / 105 / 108 / 110 / 112 / 115 / 116 / 120 / 125 / 130 / 135
Cp / 16.659 / 17.012 / 17.237 / 17.455 / 17.768 / 17.868 / 18.255 / 18.705 / 19.118 / 19.500
T K / 140 / 145 / 150 / 155 / 160 / 165 / 170 / 175 / 180 / 185
Cp / 19.852 / 20.177 / 20.477 / 20.755 / 21.014 / 21.255 / 21.480 / 21.689 / 21.886 / 22.072
T K / 190 / 195 / 200 / 205 / 208 / 210 / 211 / 214 / 215 / 217
Cp / 22.247 / 22.412 / 22.567 / 22.713 / 22.796 / 22.850 / 22.877 / 22.955 / 22.980 / 23.030
T K / 220 / 223 / 226 / 229 / 232 / 235 / 238 / 241 / 244 / 247
Cp / 23.102 / 23.170 / 23.237 / 23.303 / 23.368 / 23.431 / 23.493 / 23.554 / 23.614 / 23.672
T K / 250 / 253 / 256 / 259 / 262 / 265 / 268 / 271 / 274 / 277
Cp / 23.729 / 23.784 / 23.838 / 23.890 / 23.941 / 23.989 / 24.037 / 24.081 / 24.123 / 24.165
T K / 280 / 283 / 286 / 289 / 292 / 295 / 298 / 301 / 304 / 307
Cp / 24.207 / 24.249 / 24.290 / 24.331 / 24.372 / 24.412 / 24.451 / 24.490 / 24.528 / 24.564
T K / 310 / 313 / 316 / 319
Cp / 24.600 / 24.635 / 24.668 / 24.700
B5. Bronson et al 1933 [70]