Exponent-rules on the performance of incandescent bulbs

Exponent-rules are known to describe experimentally how the observables related to incandescent lamps alter with the change in. rated voltage. Previous works have used data on four properties of the tungsten filament viz. electrical resistivity, total radiant emittance, radiant efficacy and evaporation rate for input. parameterization as functions of temperatures; also only a few exponents were predicted. We improve over these works by (i) employing data on resistivity and emissivity only for input parameterization, (ii) deriving theoretical expressions for remaining observables viz. life, lumen as well as lumen per watt and (iii) predicting all the fourteen exponents reported by manufacturers for vacuum bulbs. Our procedure consists in assuming a steady-state operation of the bulb, parameterizing intrinsic properties of tungsten as suitable powers of temperature and eliminating the temperature between those observables for which the exponent-rules are sought. Below we summarize the values of the exponents as derived by us with those quoted by General Electric given inside brackets : a = 3.38(3.85), b=6.1(7.0); d=12.0(13.5), u=20.7(23.3), k=3.54(3.51), h=1.81(1.82), s=2.24(2.22),y=6.12(6.05), z=8.40(8.36); f=0.554(0.550), g=1.96(1.93), j=3.39(3.33), t=0.579(0.580), n=1.58(1.58).