Question

for similar light intensity, compact fluorescent bulbs use about 25% of the energy of incandescent bulbs. let's say you replaced a 75-w incandescent bulb with a fluorescent bulb and that your utility charges $0.15/kw-hour. how many dollars would you save in electricity in the 10,000-hour lifetime of the bulb?

Answer 1

The additional cost of the incandescent bulb over the fluorescent bulb over 10,000 hours is $450.

Explanation:

Let F and I stand for the energy usage for Fluorescent and Incandescent light bulbs, respectively.

We are told that for similar light intensity that:

F = 25% of I, or F = (0.25)*I

Rearrange to find I:

I = 4*F

When F = 75W, I would be 4*(75W) or 300W

The difference is 225W, the increase in energy use due to the less efficient incandescent bulb.

The utility charges $0.15/kw-hour. Watt (1 watt equals Joules/sec) is the rate of energy transfer. Total energy consumed is watts times the time, traditionally as kw-hours for the US electrical grid.

In this example, the difference in watts between the two bulbs may be multiplied by the lifetime of the bulb (in hours) to provide the additional electricity consumed by the incandescent bulb:

(300W)*(10,000 hours) = 3,000,000 W-hour

The price of electricity is measured in kilowatt-hours, so we need to convert 3,000,000 W-hours:

(3,000,000 W-hours)*(1 kw-hour)/(1,000 W-hours) [1kw-hour = 1,000 W-hours]

The additional energy consumption is 3,000 kw-hours over the expected 10,000-hour lifetime of the incandescent bulb.

At a cost of $0.15/kw-hour, the additional cost of the incandescent bulb is:

(3,000 kw-hours)*($0.15/kw-hour) = $450