The temperature depends on power delivered to your filament.

Getting the power as voltage and current product (use RMS values in case of AC driving) will let you use Stefan–Boltzmann law to get a rough estimate of filament's temperature.

As Dr. Radziwon mentioned, one uses the Stefan-Boltzmann Law, which requires the knowledge on the power delivered by the filament and its area plus the universal constant such as the Stefan Boltzmann constant, and plus the emissivity of grey body, which is the material constant dependence upon the surface properties as well as the expectation value of wave length that dominates emitted radiation compared to the black body. For Tungsten filament infrared radiation dominates, and that is about 0.34. The maximum temperature is the melting point of W, which is about 3410o C.

A typical textbook example: 

energy (Watt) = emissivity x Stefan-bolt const x Area(M2) x Temp^4

42 = 0.34 x 5.6696 × 10−8 x 1.5 × 10−5 x Temp^4

temp = 3471.615939 Kelvin = 3198.615939 Celc

.

Tungsten starts to glow at about 1000 Kelvin, at 1200 Kelvin it is red, and around 1400 Kelvin it is bright red. A tungsten filament of a glowing lightbulb (white) has a temperature of approximately 2010 K. For accurately measuring the temperature of your fialment a pyrometer would be best suited.

Dear Professor Zegenhagen, if one assumes that he/she has about the same powered 42 W light-bulb having 2010K operating temperature, one can easily calculate the emitting surface area of your Tungsten filament, and it ends up with a figure such as: 13x10-5 M2 ,which is about factor of 9 larger then ours. Therefore to reach higher operating temperatures in order to attain  more power it becomes unavoidable necessity, which of course decrease the life time.

You mentioned that you wanted the temperature to determine the mean free path (mfp).  The mfp depends on the temperature and number density of the residual gas inside the vacuum chamber, and only weakly on the temperature of the filament.  Close to the filament (on the order of a few mfp), the gas temperature will be higher but not as high as the filament.  More than a few mfp away from the filament, the gas temperature will be decreasing to close to room temperature (unless the substrate is heated.  In any case, the temperature of the filament would by hard to find from the Stefan Boltzmann theory, since you have heat losses to the filament holders (of uhknown and changing magnitude), and the heat loss due to evaporation of evaporant.   I agee with Jorg that the best way to measure the filament temperature is with a pyrometer.

Dear Fahrenbruch,  what does "a few mfp" means? Why do we have losses? I believe that Dear Oğurtani has an approximate value for temperature.

By the way I have just measured my filament's thickness. It is 1.65 mm thick. I drove 100A through this tungsten filament in my previous experiments.

Regards.

Dear Dr Fahrenbruch , There is a beautiful treatment of thermal radiation in Georg Joos, Theoretical Physics, Ch36. First of all we assumed that the light bulb is encapsulated by perfect heat insulating walls, and plus due to relatively high vacuum no heat lost through convection. Only the electrical current leads which connect filament elements to outside world should be considered for the heat lost due conduction. This may be assumed to be negligibly small. The whole system is assumed to be complete thermodynamic equilibrium in the derivation of Stefan Boltzmann Law that means input power supplied to the light bulb is equal to the power lost through the radiation.

A few questions for Murat:

1.  Why do you want to know the mean-free-path?

2.  Is the substrate heated?  What is the approximate source to substrate distance?

3.  What are the other dimensions of the filament (width, length....)?

If the chamber is at 1e-6 Torr, then the mfp would be about 130 meters so the comment that I made previously about a few mfp in the vacuum is not really relevant.   However, the pressure very close to the filament will be closer to the vapor pressure of the material being evaporated at the filament temperature.  The vapor than quickly expands  into the chamber vacuum.  Thus the mfp of the material being evaporated could affect the rate of evaporation

Dear Alan L. Fahrenbruch,

I apologize for late reply. I did not see that you asked some questions.

I answered your questions below.

1- I was curious about the mfp because I want to know what is the average distance between two particles surviving in vacuum. Actually I was looking for a solution about how to calculate it.

2-Substrate is not heated. Source and substrate are separated from each other about 12 cm.

3- Filament is attached. It has a basket in the middle. Length is 10 cm, height is higher than 1 cm.

Thanks to all researcher for their valuable contributions.

Regards.

Murat

Measure curent - voltage and calculate resistance. Rrecalculatre resistivity and compare with table data for W.