In a certain city, electricity costs $0.11 per kW- h. What is the annual cost fo
ID: 475388 • Letter: I
Question
In a certain city, electricity costs $0.11 per kW- h. What is the annual cost for electricity to power a lamp- post for 7.00 hours per day with a 100. watt incandescent light bulb an energy efficient 25-watt fluorescent bulb that produces the same amount of light? Assume 1 year = 365 days. 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?Explanation / Answer
(a) First we will tackle the 100W bulb,
Power=100W=100J/s
Thus, in 7 hours=100*7*3600J=2.52*106J
In, 1 year=365*2.52*106J=919.8*106J
But, 1kWh=3.6*106J
Thus, in 1 year the 100 W bulb will consume 255.5 kWh
At $0.11/kWh, this amounts to 0.11*255.5=$28.11/year
(b) Similarly, for the 25W bulb, it can be shown that the cost will amount to 1/4th of this amount
= 28.11*0.25=$7.03/yr
(c) To answer this, lets consider a time period of 3 years for each bulb:
Cost of 1st year for incandescent bulb= purchase cost+ running cost= $0.89+$28.11=$29
Thus, for three years it will amount to: $29*3=$87
If we buy a fluorescent bulb, we have to buy it just once for the 3 year period:
Thus, total cost for 3 years= purchase cost+3* running cost per year= $3.49+3*$7.03= $24.58
This is less than even the one year cost of an incandescent and thus, the extra cost is justified