140] 4. Analysis: Planck\'s Law and Heat Output from 100 W Incandescent Light Bu

Question

140] 4. Analysis: Planck's Law and Heat Output from 100 W Incandescent Light Bulb Use Excel and the Planck's Law formula to calculate and plot the rate of energy emitted from an incandescent tungsten halogen light bulb as a function of wavelength (W/m 2 per m versus wavelength in m). Assume the tungsten filament has a temperature of 3300 K. Sales of incandescent bulbs are being phased out because they do not meet federal energy efficiency standards of the 2007 Energy Independence and Security Act. [20] a. Show a hand written example calculation for energy emitted at 0.550 m wavelength and hand in the plot of power versus wavelength (use Excel - no hand drawn plots) with clearly labeled axis and units. [5] b. Calculate the wavelength where the irradiance maximizes and compare this answer to your plot- [5] c. What fraction of the total energy emitted by the bulb produces light that we can see and what [10] d. Compare total area under your emissive power plot to theoretical area. Given the total power do these values agree? Is your eye sensitive to this wavelength of light? fraction is wasted as heat (a>800 nm)? emitted (area under curve) estimate the surface area of the tungsten filament if the bulb is rated for 100 watts.

Explanation / Answer

Wavelength, = 0.550 m

Using Planck's Law, Energy Radiated, E is given by

E = hc/, where Planck's constant, h = 6.62607004 × 10-34 m2 kg / s,

Speed of light, c = 3 * 108  m/s

Hence, E = hc/ = 36.1422 * 10-20 m2 kg / s2

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