Hook up the light bulb in a circuit with an ammeter and voltmeter, as shown below. The bulb used (a type 44) is rated as 6.3 V at .25 A. It has a coiled filament and is gas filled. The gas filling increases the life of the bulb, but introduces a complication in the analysis.
Measure the current in the lamp and the voltage across it for voltages up to about 6 V. Don't exceed 6.3 V. Make several measurements in the range between zero and 0.1 V in order determine the room-temperature resistance.
From your data calculate the resistance of the filament from
Ohm's Law. Plot the low-current resistance versus current
(it should be a straight line) and extrapolate
the data points to zero current. The resistance at zero
current will be the room temperature value 
.
Once 
is determined,
use Eqn. (2) to calculate the temperature of the filament for
each resistance value. From the current and voltage also calculate
the power delivered to the filament at each point.
From Eqn. (1) for Stefan's Law, taking the natural logarithm of both sides gives
A plot of 
versus 
will yield a straight line with a slope of 4 and an
intercept at 
. From your data make such a plot
and you will probably notice that the lower end of the
plot is not a straight line. This is because the gas in the bulb
cools the filament by convection and so radiation is not the only
mechanism for heat loss. However, at higher power, radiation
overwhelms the convection
cooling and the log plot should be quite
linear. From the high temperature data determine the slope of your
line and compare it to the value predicted by Stefan's Law.
If a value for the emissivity is between 1/3 and 1/2, can you estimate the surface area of the filament?