Question

In a certain city, electricity costs $0.17 per kW·h. What is the annual cost for electricity to power a lamp-post for 7.50 hours per day with (a) a 100.-watt incandescent light bulb (b) an energy efficient 25-watt fluorescent bulb that produces the same amount of light? Assume 1 year = 365 days. c (c) A typical incandescent bulb costs $0.89 and lasts for about a year; a typical energy efficient fluorescent bulb costs about $3.49 and lasts for about 3 years. Is the additional cost of the fluorescent bulb justified?

Answer 1

a) 100 W = (100 W)*(1 kW/1000 W) = 0.1 kW.

The cost of electricity to power the 100 W incandescent bulb for 1 year, running 7.50 hours/day is ($0.17/kW.h)*(100 W)*(1 kW/1000 W)*(1 yr)*(365 d/1 yr)*(7.50 h/1 d) = $46.5375 ≈ $46.54 (ans).

The cost of electricity to power the energy-efficient 25 W fluorescent bulb for 1 year, running 7.50 hours/day is ($0.17/kW.h)*(25 W)*(1 kW/1000 W)*(1 yr)*(365 d/1 yr)*(7.50 h/1 d) = $11.6344 ≈ $11.63 (ans).

b) The incandescent bulb costs $0.89 while the fluorescent bulb costs $3.49. Outright, the incandescent bulb may seem as a better option due to its much cheaper price. However, consider the following two points:

i) The fluorescent bulb last thrice as much as the incandescent bulb; hence we need to replace the incandescent bulb thrice in 3 years and the total cost is ($0.89*3) = $2.67 while the fluorescent bulb runs for 3 years.

ii) Moreover, the electricity cost associated with the incandescent bulb for 3 years is ($46.54*3) = $139.62. The electricity cost associated with the fluorescent bulb for 3 years is ($11.63*3) = $34.89. Thus, the total cost associated with the incandescent bulb is ($2.67 + $139.62) = $142.29 while the cost associated with the fluorescent bulb is ($3.49 + $34.89) = $38.38. Hence, the cost associated with the fluorescent bulb is much lower than the incandescent bulb and therefore, is a better option (ans).