Chapter 1, Problem 3SP

(a)

To determine

The number of hours in one year the light is on.

Answer to Problem 3SP

The number of hours in one year the light is on is $\text{1750}\text{hr}$.

Explanation of Solution

Given Info: A bulb is switched on for $5\text{h}$, for $350$ days.

Write the expression for the total time the light is on.

$t=\text{number of days}\times \text{hours the light is on}$

Here,

$t$ is the total time the light is on

Substitute 5 hr for the hours the light is on and 350 for the number of days to find the total time the light is on.

$\begin{array}{c}t=5\text{hr}\times \text{350}\\ =1\text{750}\text{hr}\end{array}$

Conclusion:

Therefore, the number of hours in one year the light is onis $\text{1750}\text{hr}$.

(b)

To determine

The energy in kilowatt-hour.

Answer to Problem 3SP

The energy in kilowatt-hour is $131.250\text{kW-hr}$.

Explanation of Solution

Given Info: A bulb is switched on for $5\text{h}$, for $350$ days.

Write the expression for the energy.

$E=Pt$

Here,

$E$ is the energy

$P$ is the power

$t$ is the time

Substitute $75\text{W}$ for $P$ and $\text{1750}\text{hr}$ for $t$ to get $E$.

$\begin{array}{c}E=\left(75\text{W}\right)\left(\text{1,750}\text{hr}\right)\\ =131,250\text{W-hr}\times \frac{1\text{kW-hr}}{1,000\text{W-hr}}\\ =131.250\text{kW-hr}\end{array}$

Conclusion:

Therefore, the energy in kilowatt-hour is $131.250\text{kW-hr}$.

(c)

To determine

The energy in kilowatt-hour for a $15\text{W}$ bulb.

Answer to Problem 3SP

The energy in kilowatt-hour is $26.250\text{kW-hr}$.

Explanation of Solution

Given Info: A bulb is switched on for $5\text{h}$, for $350$ days.

Write the expression for the energy.

$E=Pt$

Substitute $15\text{W}$ for $P$ and $\text{1750}\text{hr}$ for $t$ to get $E$.

$\begin{array}{c}E=\left(15\text{W}\right)\left(\text{1,750}\text{hr}\right)\\ =26,250\text{W-hr}\times \frac{1\text{kW-hr}}{1,000\text{W-hr}}\\ =26.250\text{kW-hr}\end{array}$

Conclusion:

Therefore, the energy in kilowatt-hour is $26.250\text{kW-hr}$.

(d)

To determine

The cost of using $75\text{W}$ bulb.

Answer to Problem 3SP

The cost of using $75\text{W}$ bulb is $\text{\$}19.69$.

Explanation of Solution

Given Info: The cost of electricity is $15¢/\text{kW-hr}$.

Write the expression for the total cost.

$\text{Cost for 75-W bulb}=\text{Energy in kW-hr}\times \text{cost per kW-hr}$

Substitute $131.250\text{kW-hr}$ for the energy in kW-hr and $15¢/\text{kW-hr}$ for the cost per kW-hr.

$\begin{array}{c}\text{Cost}\text{for 75-W bulb}=131.250\text{kW-hr}\times 15¢/\text{kW-hr}\\ =1968.75¢\times \frac{1\text{\$}}{100¢}\\ =\text{\$}19.6875\\ \approx \text{\$}19.69\end{array}$

Conclusion:

Therefore, the cost of using $75\text{W}$ bulb is $\text{\$}19.69$.

(e)

To determine

The cost of using $15\text{W}$ bulb.

Answer to Problem 3SP

The cost of using $15\text{W}$ bulb is $\text{\$}3.94$.

Explanation of Solution

Given Info: The cost of electricity is $15¢/\text{kW-hr}$.

Write the expression for the total cost.

$\text{Cost for 15-W bulb}=\text{Energy in kW-hr}\times \text{cost per kW-hr}$

Substitute $26.250\text{kW-hr}$ for the energy in kW-hr and $15¢/\text{kW-hr}$ for the cost per kW-hr.

$\begin{array}{c}\text{Cost for 15-W bulb}=26.250\text{kW-hr}\times 15¢/\text{kW-hr}\\ =393.75¢\times \frac{1\text{\$}}{100¢}\\ =\text{\$}3.9375\\ \approx \text{\$}3.94\end{array}$

Conclusion:

Therefore, the cost of using $15\text{W}$ bulb is $\text{\$}3.94$.

(f)

To determine

The savings made by using $15\text{W}$ bulb.

Answer to Problem 3SP

The savings made by using $15\text{W}$ bulb is $\text{\$}15.75$.

Explanation of Solution

Given Info: The cost of electricity is $15¢/\text{kW-hr}$.

Write the expression for the savings made.

$\text{Savings = Cost for75-W}\text{bulb}-\text{Cost for15-W}\text{bulb}$

Substitute $\text{\$}19.69$ for the cost for 75-W bulb and $\text{\$}3.94$ for the cost for the 15-W bulb.

$\begin{array}{c}\text{Savings}=\text{\$}19.6875-\text{\$}3.9375\\ =\text{\$}15.75\end{array}$

Conclusion:

Therefore, the cost of using $15\text{W}$ bulb is $\text{\$}15.75$.

(e)

To determine

The savings made by using twenty $15\text{W}$ bulb.

Answer to Problem 3SP

The savings made by using twenty $15\text{W}$ bulb is $\text{\$}315$.

Explanation of Solution

Given Info: The cost of electricity is $15¢/\text{kW-hr}$.

Write the expression for the total savings made.

$\text{Total savings}=\text{savings from using one 15-W bulb}\times \text{20}$

Substitute $\text{\$}15.75$ for the savings using one 15-W bulb.

$\begin{array}{c}\text{Total savings}=\text{\$}15.75\times 20\\ =\text{\$}315\end{array}$

Conclusion:

Therefore, the savings made by using twenty $15\text{W}$ bulb is $\text{\$}315$.