3
5.2 Measurement of radiant intensity as a
function of the temperature of the fila-
ment
Connect the thermopile to the P3340 digital
multimeter (1002785).
Set up the Stefan-Boltzmann lamp in front
of the thermopile and connect up the DC
power supply and the two P1035 digital mul-
timeters (1002781).
Apply a voltage in steps of 1 V up to a max-
imum of 12 V, measure the lamp voltage U,
the lamp current I, and use the thermopile
to measure the radiant intensity (5.3,
Tab. 2).
5.3 Evaluation
Calculate R = U/I (Tab. 2).
Now the values determined, Tref, Rref, R, can
be used along with the temperature coeffi-
cient of resistance for tungsten
= 4.4 · 10-3 K-1 to calculate the tempera-
ture of the filament by means of the follow-
ing formula (Tab. 2):
ref
ref
ref T
R
RR
T
.
One possible alternative method for determin-
ing the temperature T of the filament is to calcu-
late the quotients R/Rref and then use Fig. 2 or
Tab. 3 to find the temperature.
Note: In Table 3 the quotient R/Rref is specified
for Tref = 300 K and for Tref = 290 K. It is possible
to determine the temperature more precisely by
interpolating between these two reference val-
ues to take account of the actual room temper-
ature.
Plot as a function of T4 (Fig. 3).
Tab. 2: Values for the resistance R and the tempera-
ture T of the filament calculated from the
measured values for the lamp voltage U and
the lamp current I, as well as the radiated in-
tensity measured with the thermopile
U / V I / A R / Ω T / K
/ V
0.00369 0.006 0.615 328 0
1.0502 0.554 1.896 854 0.0001
2.033 0.706 2.879 1259 0.0004
3.012 0.837 3.599 1554 0.0011
4.003 0.958 4.178 1792 0.0019
5.012 1.071 4.679 1998 0.0029
6.017 1.174 5.125 2181 0.0042
7.074 1.276 5.5434 2353 0.0058
8.028 1.362 5.894 2497 0.0072
9.011 1.446 6.232 2636 0.0088
10.088 1.534 6.576 2777 0.0106
11.02 1.607 6.8575 2893 0.0125
11.685 1.68 6.955 2933 0.0145
