Question

6. An incandescent light bulb operates at 100 Watts. Let's assume all the power is emitted as light (most of which will be infrared). The output peaks at a wavelength Amax 1317 nm. a. What is the temperature of the filament? b. What is the total surface area of the filament? (You can assume ε-1.)

Answer 1

Light bulb at 100 watts a) According to given displacement law, lambda_mT = constant = C where C = 2.898 times 10^-3 mk given lambda_m = 1317 mm T = 2.898 times 10^-3/13.7 times 10^-9 = 2200 k T = 2200 k b) According to Stefan's law epsilon = 1 total power radiated from an object by its surface area P = A sigma T^4 Given P = 100 watts \r\n sigma value is sigma = 5.67 times 10^-8 wn^-2 T^-4 100 = A(5.67 times 10^-8)(2200)^4 A = 100/5.67 times 10^-8 times 1/(2200)^4 A = 3.64 times 10^-6/10^-8 = 3.64 times 100^+ 2 = 3.64 times 100 A = 3643 m^2