Chapter 1, Problem 3SP

A compact fluorescent light (CFL) bulb is very energy-efficient. A 22W CFL bulb has the same brightness as a 100W incandescent bulb. (Note that these calculations ignore the fact that the CFL bulb can last up to 10 times as long as the incandescent bulb. This would increase your savings even more.)

1. a. If you have this light bulb on for 5 hours a day, for 350 days during a year, how many hours is it on?
2. b. A kilowatt is 1000 watts. The kilowatt-hour is a common unit for energy, obtained by multiplying the power in kilowatts by the time used in hours. How many kilowatt-hours (kWh) will you use when burning the 100W bulb for the year (don’t forget to convert the 100W to kW first)?
3. c. How many kilowatt-hours (kWh) will you use when burning the 22W bulb for the year (be sure to convert the 22W to kW before multiplying by the time in hours)?
4. d. Assuming that the cost of electricity is 15¢ per kWh, what is the cost of using the 100W incandescent bulb for the year?
5. e. Assuming this same cost, what is the cost of using the 22W CFL bulb for the year?
6. f. How much do you save per year by using the 22W CFL bulb?
7. g. How much would you save every year if you replaced 20 of the 100W incandescent bulbs with the 22W CFL bulbs?

To determine

The number of hours the light bulb is on.

Answer to Problem 3SP

The number of hours the light bulb is on is $1750\text{hours}$.

Explanation of Solution

Given info: Light bulb is on for 5 hours a day for 350 days during a year.

The number of hours the light bulb is on is,

$\begin{array}{l}\left(\frac{5\text{hours}}{1\text{day}}\right)\left(350\text{days}\right)\\ =1750\text{hours}\end{array}$

Conclusion:

The number of hours the light bulb is on is $1750\text{hours}$.

To determine

The number of kilo-watt hours used when the light bulb is on for a year.

Answer to Problem 3SP

The number of kilo-watt hours used when the light bulb is on for a year is $175\text{kWh}$.

Explanation of Solution

Given info: Light bulb is on for 5 hours a day for 350 days during a year.

From (a), the number of hours the light bulb is on is $1750\text{hours}$

The number of kilo-watt hours used when the light bulb is on for a year is,

$\begin{array}{l}\left(100\text{W}\right)\left(\frac{1\text{kW}}{1000\text{W}}\right)\left(1750\text{hours}\right)\\ =175\text{kWh}\end{array}$

Conclusion:

The number of kilo-watt hours used when the light bulb is on for a year is $175\text{kWh}$.

To determine

The number of kilo-watt hours used when the 22 W light bulb is on for a year.

Answer to Problem 3SP

The number of kilo-watt hours used when the 22 W light bulb is on for a year is $38.5\text{kWh}$.

Explanation of Solution

Given info: Light bulb is on for 5 hours a day for 350 days during a year.

From (a), the number of hours the light bulb is on is $1750\text{hours}$

The number of kilo-watt hours used when the 22 W light bulb is on for a year is,

$\begin{array}{l}\left(22\text{W}\right)\left(\frac{1\text{kW}}{1000\text{W}}\right)\left(1750\text{hours}\right)\\ =38.5\text{kWh}\end{array}$

Conclusion:

The number of kilo-watt hours used when the 22 W light bulb is on for a year is $38.5\text{kWh}$.

To determine

The cost of using 100 W bulb for a year.

Answer to Problem 3SP

The cost of using 100 W bulb for a year is $2625\not\subset$.

Explanation of Solution

Given info: Cost of electricity is $15\not\subset$ per kWh.

From (b), number of kilo-watt hours used when the 100 W light bulb is on for a year is $175\text{kWh}$

The cost of using 100 W bulb for a year is,

$\begin{array}{l}\left(\frac{15\not\subset }{1\text{kWh}}\right)\left(175\text{kWh}\right)\\ =2625\not\subset \end{array}$

Conclusion:

The cost of using 100 W bulb for a year is $2625\not\subset$.

To determine

The cost of using 22 W bulb for a year.

Answer to Problem 3SP

The cost of using 22 W bulb for a year is $577.5\not\subset$.

Explanation of Solution

Given info: Cost of electricity is $15\not\subset$ per kWh.

From (b), number of kilo-watt hours used when the 22 W light bulb is on for a year is $175\text{kWh}$

The cost of using 22 W bulb for a year is,

$\begin{array}{l}\left(\frac{15\not\subset }{1\text{kWh}}\right)\left(38.5\text{kWh}\right)\\ =577.5\not\subset \end{array}$

Conclusion:

The cost of using 22 W bulb for a year is $577.5\not\subset$.

To determine

The savings per year while using 22 W CFL bulb.

Answer to Problem 3SP

The savings per year while using 22 W CFL bulb is $2047.5\not\subset \text{/yr}$.

Explanation of Solution

Given info: Cost of electricity is $15\not\subset$ per kWh.

The savings per year while using 22 W CFL bulb is the difference between the cost of using 100 W and 22 W bulbs. Therefore, the saving is given by,

$\begin{array}{l}\left(2625\not\subset \right)-\left(577.5\not\subset \right)\\ =2047.5\not\subset \text{/yr}\end{array}$

Conclusion:

The savings per year while using 22 W CFL bulb is $2047.5\not\subset \text{/yr}$.

To determine

The savings per year while twenty 100 W bulbs are replaced by 22 W CFL bulb.

Answer to Problem 3SP

The savings per year while twenty 100 W bulbs are replaced by 22 W CFL bulb is $40950\not\subset \text{/yr}$.

Explanation of Solution

Given info: Cost of electricity is $15\not\subset$ per kWh.

The savings per year while using 22 W CFL bulb is $2047.5\not\subset \text{/yr}$. Therefore, when twenty 100 W bulbs are replaced by 22 W CFL bulbs, the savings is,

$\begin{array}{l}\left(2047.5\not\subset \text{/yr}\right)\left(20\right)\\ =40950\not\subset \text{/yr}\end{array}$

Conclusion:

The savings per year while twenty 100 W bulbs are replaced by 22 W CFL bulb is $40950\not\subset \text{/yr}$.