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How hot does a filament light bulb get?

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Hot, really hot. Typically in the range of about 2000C to 2500C (3600F - 4500F). It would be pretty difficult to directly measure the temperature of the filament so you have to use something other than a thermometer for the measurement. It should be possible to estimate the temperature of the filament from the light spectrum. Basically, treat the light bulb like a perfect black body radiator and use Plank's Law (http://en.wikipedia.org/wiki/Planck%27s_law) and the light spectrum of the bulb (for example http://www.graphics.cornell.edu/online/measurements/source-spectra/index.html) to calculate the temperature. Another way, which is a bit easier, is to use basic electronic theory to calculate the temperature of the filament that is required to produce the manufacturer's specifications for the bulb. For example, consider a typical 100 watt, 120 VAC light bulb with a tungsten filament. The bulb consumes (and radiates) 100 watts of power. A light bulb is a purely resistive load so Power=(Voltage)*(Current). Plugging in 100 watts as the power, 120 as the voltage (actually, that's the RMS voltage), and solving for current we get an RMS current of 0.83 amps. Since the bulb is just a resistor it obeys Ohm's Law; Voltage=(Current)*(Resistance). Our voltage is 120 and we determined the current to be 0.83 amps, so the resistance of the bulb when it is operating is 120/0.83= 144 ohms. If you take a 100W incandescent light bulb and measure its resistance at room temperature you get a value of about 15 Ohms. The difference between the room temperature resistance and the resistance when the bulb is operating is due to the affect of temperature on the filament's resistance. Metals (and conductors in general) increase their resistance as they are heated. The resistance at a particular temperature can be calculated with; R=Rref*(1 + alpha(T-Tref)] Where, R is the resistance at temperature T degrees Celsius. Rref is the resistance at a standard temperature Tref (often 0C or 20C). Alpha is the "temperature coefficient of resistance" for the material. For tungsten alpha=0.0044/C with a Tref of 20C (68F). If we assume that the 15 Ohm resistance at room temperature is close enough to the value at 20C (68F) then we can use Rref=15 ohms and R is the 144 ohms we calculated from the wattage and voltage of the bulb. Plugging these numbers into the equation; 144=15*(1 + 0.0044*(T - 20)) Solving for T (the temperature required to get the filament's resistance to 144 ohms) we get T=1975C (about 3600F). That's pretty hot! The filaments temperature will change if the applied voltage changes. The temperature will also be different from light bulb to light bulb (even if they have the same voltage and wattage ratings) since no two bulbs are exactly alike. An individual bulb will also change as it ages and as a function of the temperature outside the bulb.
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