Final answer:
To determine the efficiency of a 100 watts, 230 volts gas-filled lamp with a mean spherical candle power of 92, we converted candelas to lumens and then divided by the wattage to find that the lamp's efficiency is approximately 11.52 lumens per watt.
Step-by-step explanation:
The question involves calculating the efficiency of a gas-filled lamp in terms of lumens per watt. To find the efficiency, we need to convert the mean spherical candle power (candela) to lumens. The mean spherical candle power given is 92, which means the lamp emits 92 candelas of light intensity. The conversion between candelas and lumens involves the solid angle in steradians that the light covers. Since 1 candela equals 1 lumen per steradian, and a full sphere covers 4π steradians, we multiply 92 candelas by 4π to find the total luminous flux in lumens.
Therefore, the total luminous flux, P, is 92 candela × 4π steradians. This results in approximately 1152 lumens. To find the efficiency in lumens per watt, we divide the total luminous flux by the power of the lamp in watts, which is 100 W.
Efficiency = Luminous Flux (lm) / Power (W) = 1152 lm / 100 W = 11.52 lumens per watt.