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Showing energy distribution of a black body radiator. In the third column is tabulated the proportion of energy emitted by a black body radiator at temperature T in the spectral region between wave lengths zero and λ microns.
Product of wave length λ in microns times absolute temperature in degrees Kelvin. λT in micron degrees.
Spectral intensity of radiation in terms of maximum, according to Frehafer and Snow*Eλ/Em (See equation 9)
Proportion of spectral energy in region from ultraviolet limit to λT (See equation 13)
400
7.367×10−10
420
3.185×10−9
8.013×10−12
440
1.193×10−8
3.947×10−11
460
3.943×10−8
1.480×10−10
480
1.171×10−7
4.828×10−10
500
3.154×10−7
1.417×10−9
520
7.818×10−7
3.805×10−9
540
1.799×10−6
9.466×10−9
560
3.874×10−6
2.197×10−8
580
7.869×10−6
4.797×10−8
600
1.514×10−5
9.907×10−8
620
2.781×10−5
1.949×10−7
640
4.889×10−5
3.664×10−7
660
8.275×10−5
6.614×10−7
680
1.351×10−4
1.150×10−6
700
2.135×10−4
1.935×10−6
720
3.276×10−4
3.155×10−6
740
4.897×10−4
5.014×10−6
760
7.136×10−4
7.751×10−6
780
1.018×10−3
1.169×10−5
800
1.419×10−3
1.723×10−5
840
2.615×10−3
3.525×10−5
880
4.503×10−3
6.718×10−5
900
5.785×10−3
9.051×10−5
920
7.326×10−3
1.204×10−4
960
1.134×10−2
2.046×10−4
1000
1.682×10−2
3.318×10−4
1050
2.609×10−2
5.742×10−4
1080
3.314×10−2
7.764×10−4
1120
4.441×10−2
1.128×10−3
1160
5.794×10−2
1.593×10−3
1200
7.391×10−2
2.192×10−3
1250
9.720×10−2
3.161×10−3
1300
.1243
4.421×10−3
1400
.1887
7.962×10−3
1500
.2647
.01311
1600
.3486
.02007
1700
.4363
.02900
1800
.5241
.03993
1900
.6086
.05282
2000
.6871
.06757
2100
.7579
.08402
2200
.8196
.1020
2300
.8719
.1212
2400
.9147
.1416
2500
.9479
.1628
2600
.9722
.1846
2700
.9888
.2069
2800
.9974
.2296
2890
1.0000
.2500
3000
.9967
.2750
3100
.9886
.2976
3200
.9762
.3200
3300
.9603
.3420
3400
.9418
.3636
3500
.9209
.3848
3600
.8982
.4055
3700
.8742
.4257
3800
.8492
.4453
3900
.8236
.4643
4000
.7975
.4827
4200
.7453
.5178
4400
.6938
.5506
4600
.6440
.5810
4800
.5967
.6092
5000
.5521
.6353
5400
.4715
.6818
5800
.4023
.7215
6000
.3716
.7392
6400
.3177
.7705
6800
.2723
.7973
7000
.2523
.8092
7400
.2173
.8305
7600
.2019
.8401
7800
.1878
.8489
8000
.1748
.8572
8400
.1519
.8720
8800
.1324
.8850
9000
.8908
9200
.1159
.8963
9600
.1018
.9062
10000
.08970
.9149
10800
.07036
.9294
11600
.05588
.9408
12400
.04488
.9499
13200
.03644
.9573
14000
.02986
.9633
14800
.02469
.9683
15600
.02059
.9724
16000
.01886
.9742
17000
.01525
.9781
18000
.01246
.9812
19000
.01027
.9838
20000
.008548
.9859
21000
.9877
Infinity
0
1.
loc. cit.
Table 2
Proportions of spectral energy emitted in the far ultraviolet, near ultraviolet, visible and infrared regions of the spectrum of a black body radiator at various temperatures.
Temperature of black body radiator, in degrees K.
Per cent of spectral energy emitted in various regions of the spectrum of a black body radiator.
Far U.V. or λ0 to λ3000A
Near U.V. or λ3000 to λ4000
Visible or λ4000 to λ7600
Infrared or λ7600 to infinity
Total spectrum or λ0 to infinity
1000°K
0.0000
0.0000
0.001
100.0
100
1500
0.0000
0.0000
0.115
99.9
100
1800
0.0000
0.0003
0.668
99.3
100
2000
0.0000
0.0017
1.43
98.6
100
2200
0.0001
0.0067
2.62
97.4
100
2400
0.0003
0.020
4.28
95.7
100
2500
0.0006
0.032
5.25
94.7
100
2600
0.0012
0.051
6.35
93.6
100
2700
0.0021
0.076
7.41
92.5
100
2800
0.0035
0.109
8.78
91.1
100
2900
0.0058
0.153
10.13
89.7
100
3000
0.0091
0.210
11.51
88.3
100
3100
0.0138
0.281
12.97
86.7
100
3200
0.0205
0.369
14.44
85.2
100
3300
0.0296
0.472
15.95
83.5
100
3500
0.057
0.74
19.00
80.2
100
4000
0.219
1.79
26.39
71.6
100
5000
1.31
5.45
37.77
55.5
100
6000
3.99
10.17
43.36
42.5
100
8000
14.16
17.84
42.59
25.4
100
10000
27.5
20.77
35.74
16.0
100
12000
40.5
20.37
28.49
10.6
100
15000
56.6
17.31
19.89
6.2
100
20000
73.9
11.80
11.32
2.96
100
Table 3
Data on tungsten compiled from various published data by W. E. Forsythe and A. G. Worthing, together with comparative values of factor G for the visible spectrum as computed by use of either emissivity or luminous efficiency data. According to equations 19 and 23, G is the factor by which the proportion of energy in a given region of the spectrum of a black body at temperature Tc must be multiplied in order to obtain the proportion of energy emitted in the same spectral region by tungsten when of color temperature Tc.
Temperature of tungsten filament in deg. K
Emissivities
Luminous efficiency in lumens per watt.
Computed value of factor G for the visible spectrum.
True temp. T
Color temp. Tc
Color emis. ∊c
Total emis. ∊t
Tungsten at temp. T l1
Black body at temp. Tc l
1500
1517
.383
.192
0.20
2.09
1800
1825
.376
.236
1.16
.67
1.64
1.73
2000
2033
.370
.260
2.78
1.75
1.52
1.59
2200
2242
.364
.279
5.47
3.67
1.41
1.49
2400
2452
.350
.296
9.37
6.70
1.29
1.40
2600
2663
.353
.311
14.28
10.8
1.25
1.32
2800
2878
.347
.323
20.43
16.0
1.20
1.28
3000
3094
.343
.334
27.1
22.1
1.16
1.22
3200
3311
.338
.341
34.6
28.9
1.14
1.19
3300
3422
.335
.344
38.5
1.13
3400
3533
.332
.348
42.6
1.12
3500
3646
.329
.351
45.9
1.10
3655
3817
.324
.354
53.1
1.09
Table 4
Data on sundry non-black body radiators, according to E. P. Hyde, together with computed values of factor G for the visible spectrum.
Type of radiator
Color temp. of radiator in degrees K Tc
Luminous efficiency in lumens per watt
Computed value of factor G, for the visible spectrum or
Non-black body radiator at temp. T
Black body raddiator at temp. Tc
l1
l
Black body
1700
0.34
.34
1.
“ ”
2160
2.8
2.8
1.
Untreated carbon
2160
3.5
2.8
1.25
“ “ “
1700
.39
.34
1.15
Flashed carbon
1700
.41
.34
1.20
“ “
2160
3.7
2.8
1.32
Graphitized carbon
1700
.41
.34
1.20
“ “
2160
3.7
2.8
1.32
Osmium
1700
.72
.34
2.12
“
2160
4.9
2.8
1.75
Tantalum
1700
.5
.34
1.47
“
2160
3.9
2.8
1.39
Tungsten
1700
.59
.34
1.73
“
2160
4.4
2.8
1.57
Table 5
Data on various types of incandescent lamps and computed values of factor G for the visible spectrum and the proportion of total energy emitted by tungsten in the visible spectrum (λ4000 to λ7000).
Lamp
Lumens emitted per watt l1
Maximum temperature in deg. K
Average color temp. Tc in deg. K
Maximum brightness of filament candles/(cm)2b1
Probable value of factor G for the visible spectrum G
Proportion of total radiant energy emitted ia the visible spectrum
by a black body at temp. Tcϕυ
by a non-black body radiator Gϕυ
(Vacuum lamps)
50-watt carbon
2065
1.25
.01776
.022
50-watt gem
2130
1.25
.02157
.027
2.5-w.p.c. gem
2195
1.25
.02587
.032
4-w.p.c. carbon
2080
1.25
.01869
.023
3.1-w.p.c. carbon
2165
1.20
.02379
.028
2-w.p.c. osmium
2185
1.72
.02513
.043
50-watt tantalum
2300
1.23
.03388
.042
2-w.p.c. tantalum
2260
1.24
.03062
.038
1.25-w.p.c. tungsten
2400
1.33
.04265
.057
10-watt tungsten
8.
2410
1.32
.04363
.058
2S-watt “
9.8
2450
1.31
.04743
.062
40-watt “
10.0
2460
1.30
.04747
.062
60-watt “
10.1
2465
1.30
.04885
.063
(Regular gas-filled tungsten lamps)
50-watt tungsten
10.0
2685
2670
469
1.25
.07165
.090
75-watt
11.8
2735
2705
563
1.24
.07592
.094
100-watt
12.9
2760
2740
605
1.23
.08020
.099
200-watt
15.2
2840
2810
781
1.22
.08897
.109
300-watt
16.3
2870
2840
862
1.21
.09314
.113
500-watt
18.1
2930
2920
1015
1.20
.1003
.120
1000-watt
20.0
2990
2980
1225
1.19
.1122
.133
2000-watt
21.2
3020
3000
1350
1.18
.1151
.136
(Special tungsten lamps.) 1000-watt stereopticon
24.2
3185
3175
2065
1.16
.1407
.163
900-watt movie
27.3
3290
3220
2660
1.15
.1476
.170
10-KW.
31.0
3350
3300
3050
1.14
.1595
.182
30-KW.
31.0
3350
3300
3050
1.14
.1595
.182
Tables (5)
Table 1
Showing energy distribution of a black body radiator. In the third column is tabulated the proportion of energy emitted by a black body radiator at temperature T in the spectral region between wave lengths zero and λ microns.
Product of wave length λ in microns times absolute temperature in degrees Kelvin. λT in micron degrees.
Spectral intensity of radiation in terms of maximum, according to Frehafer and Snow*Eλ/Em (See equation 9)
Proportion of spectral energy in region from ultraviolet limit to λT (See equation 13)
400
7.367×10−10
420
3.185×10−9
8.013×10−12
440
1.193×10−8
3.947×10−11
460
3.943×10−8
1.480×10−10
480
1.171×10−7
4.828×10−10
500
3.154×10−7
1.417×10−9
520
7.818×10−7
3.805×10−9
540
1.799×10−6
9.466×10−9
560
3.874×10−6
2.197×10−8
580
7.869×10−6
4.797×10−8
600
1.514×10−5
9.907×10−8
620
2.781×10−5
1.949×10−7
640
4.889×10−5
3.664×10−7
660
8.275×10−5
6.614×10−7
680
1.351×10−4
1.150×10−6
700
2.135×10−4
1.935×10−6
720
3.276×10−4
3.155×10−6
740
4.897×10−4
5.014×10−6
760
7.136×10−4
7.751×10−6
780
1.018×10−3
1.169×10−5
800
1.419×10−3
1.723×10−5
840
2.615×10−3
3.525×10−5
880
4.503×10−3
6.718×10−5
900
5.785×10−3
9.051×10−5
920
7.326×10−3
1.204×10−4
960
1.134×10−2
2.046×10−4
1000
1.682×10−2
3.318×10−4
1050
2.609×10−2
5.742×10−4
1080
3.314×10−2
7.764×10−4
1120
4.441×10−2
1.128×10−3
1160
5.794×10−2
1.593×10−3
1200
7.391×10−2
2.192×10−3
1250
9.720×10−2
3.161×10−3
1300
.1243
4.421×10−3
1400
.1887
7.962×10−3
1500
.2647
.01311
1600
.3486
.02007
1700
.4363
.02900
1800
.5241
.03993
1900
.6086
.05282
2000
.6871
.06757
2100
.7579
.08402
2200
.8196
.1020
2300
.8719
.1212
2400
.9147
.1416
2500
.9479
.1628
2600
.9722
.1846
2700
.9888
.2069
2800
.9974
.2296
2890
1.0000
.2500
3000
.9967
.2750
3100
.9886
.2976
3200
.9762
.3200
3300
.9603
.3420
3400
.9418
.3636
3500
.9209
.3848
3600
.8982
.4055
3700
.8742
.4257
3800
.8492
.4453
3900
.8236
.4643
4000
.7975
.4827
4200
.7453
.5178
4400
.6938
.5506
4600
.6440
.5810
4800
.5967
.6092
5000
.5521
.6353
5400
.4715
.6818
5800
.4023
.7215
6000
.3716
.7392
6400
.3177
.7705
6800
.2723
.7973
7000
.2523
.8092
7400
.2173
.8305
7600
.2019
.8401
7800
.1878
.8489
8000
.1748
.8572
8400
.1519
.8720
8800
.1324
.8850
9000
.8908
9200
.1159
.8963
9600
.1018
.9062
10000
.08970
.9149
10800
.07036
.9294
11600
.05588
.9408
12400
.04488
.9499
13200
.03644
.9573
14000
.02986
.9633
14800
.02469
.9683
15600
.02059
.9724
16000
.01886
.9742
17000
.01525
.9781
18000
.01246
.9812
19000
.01027
.9838
20000
.008548
.9859
21000
.9877
Infinity
0
1.
loc. cit.
Table 2
Proportions of spectral energy emitted in the far ultraviolet, near ultraviolet, visible and infrared regions of the spectrum of a black body radiator at various temperatures.
Temperature of black body radiator, in degrees K.
Per cent of spectral energy emitted in various regions of the spectrum of a black body radiator.
Far U.V. or λ0 to λ3000A
Near U.V. or λ3000 to λ4000
Visible or λ4000 to λ7600
Infrared or λ7600 to infinity
Total spectrum or λ0 to infinity
1000°K
0.0000
0.0000
0.001
100.0
100
1500
0.0000
0.0000
0.115
99.9
100
1800
0.0000
0.0003
0.668
99.3
100
2000
0.0000
0.0017
1.43
98.6
100
2200
0.0001
0.0067
2.62
97.4
100
2400
0.0003
0.020
4.28
95.7
100
2500
0.0006
0.032
5.25
94.7
100
2600
0.0012
0.051
6.35
93.6
100
2700
0.0021
0.076
7.41
92.5
100
2800
0.0035
0.109
8.78
91.1
100
2900
0.0058
0.153
10.13
89.7
100
3000
0.0091
0.210
11.51
88.3
100
3100
0.0138
0.281
12.97
86.7
100
3200
0.0205
0.369
14.44
85.2
100
3300
0.0296
0.472
15.95
83.5
100
3500
0.057
0.74
19.00
80.2
100
4000
0.219
1.79
26.39
71.6
100
5000
1.31
5.45
37.77
55.5
100
6000
3.99
10.17
43.36
42.5
100
8000
14.16
17.84
42.59
25.4
100
10000
27.5
20.77
35.74
16.0
100
12000
40.5
20.37
28.49
10.6
100
15000
56.6
17.31
19.89
6.2
100
20000
73.9
11.80
11.32
2.96
100
Table 3
Data on tungsten compiled from various published data by W. E. Forsythe and A. G. Worthing, together with comparative values of factor G for the visible spectrum as computed by use of either emissivity or luminous efficiency data. According to equations 19 and 23, G is the factor by which the proportion of energy in a given region of the spectrum of a black body at temperature Tc must be multiplied in order to obtain the proportion of energy emitted in the same spectral region by tungsten when of color temperature Tc.
Temperature of tungsten filament in deg. K
Emissivities
Luminous efficiency in lumens per watt.
Computed value of factor G for the visible spectrum.
True temp. T
Color temp. Tc
Color emis. ∊c
Total emis. ∊t
Tungsten at temp. T l1
Black body at temp. Tc l
1500
1517
.383
.192
0.20
2.09
1800
1825
.376
.236
1.16
.67
1.64
1.73
2000
2033
.370
.260
2.78
1.75
1.52
1.59
2200
2242
.364
.279
5.47
3.67
1.41
1.49
2400
2452
.350
.296
9.37
6.70
1.29
1.40
2600
2663
.353
.311
14.28
10.8
1.25
1.32
2800
2878
.347
.323
20.43
16.0
1.20
1.28
3000
3094
.343
.334
27.1
22.1
1.16
1.22
3200
3311
.338
.341
34.6
28.9
1.14
1.19
3300
3422
.335
.344
38.5
1.13
3400
3533
.332
.348
42.6
1.12
3500
3646
.329
.351
45.9
1.10
3655
3817
.324
.354
53.1
1.09
Table 4
Data on sundry non-black body radiators, according to E. P. Hyde, together with computed values of factor G for the visible spectrum.
Type of radiator
Color temp. of radiator in degrees K Tc
Luminous efficiency in lumens per watt
Computed value of factor G, for the visible spectrum or
Non-black body radiator at temp. T
Black body raddiator at temp. Tc
l1
l
Black body
1700
0.34
.34
1.
“ ”
2160
2.8
2.8
1.
Untreated carbon
2160
3.5
2.8
1.25
“ “ “
1700
.39
.34
1.15
Flashed carbon
1700
.41
.34
1.20
“ “
2160
3.7
2.8
1.32
Graphitized carbon
1700
.41
.34
1.20
“ “
2160
3.7
2.8
1.32
Osmium
1700
.72
.34
2.12
“
2160
4.9
2.8
1.75
Tantalum
1700
.5
.34
1.47
“
2160
3.9
2.8
1.39
Tungsten
1700
.59
.34
1.73
“
2160
4.4
2.8
1.57
Table 5
Data on various types of incandescent lamps and computed values of factor G for the visible spectrum and the proportion of total energy emitted by tungsten in the visible spectrum (λ4000 to λ7000).
Lamp
Lumens emitted per watt l1
Maximum temperature in deg. K
Average color temp. Tc in deg. K
Maximum brightness of filament candles/(cm)2b1
Probable value of factor G for the visible spectrum G
Proportion of total radiant energy emitted ia the visible spectrum