Chapter 22, Problem 81A

To determine

The monthly heating bill if the electricity costs $\$0.10\text{per kWh}$ .

Answer to Problem 81A

  $\$216$

Explanation of Solution

Given:

The electricity costs, $C=\$0.10\text{per kWh}$

The number of days, thermostat is expected to run, $t=\left(\frac{1}{4}\times 30\text{days}\right)=7.5\text{days}$

From the given figure,

The resistance, $R=4.80\Omega$

The potential of the battery, $V=240.0\text{V}$

Formula used:

The thermal energy $\left(E\right)$ during time $t$ is given by,

  $\begin{array}{c}E=VIt\\ =\frac{V^{2}t}{R}\end{array}$

Where,I is the current, V is the potential and R is the resistance.

Calculation:

Using the above formula, the energy consumed will be,

  $\begin{array}{c}E=\frac{V^{2}t}{R}\\ =\frac{{\left(240\right)}^2\left(7.5\text{days}\right)}{4.8}\times \frac{24\text{h}}{1\text{day}}\\ =2160\text{kWh}\end{array}$

And, then the monthly bill will be,

  $\begin{array}{c}\text{Cost}=C\times E\\ =\left(\$0.10\right)\left(2160\right)\\ =\$216\end{array}$

Conclusion:

Hence, the monthly heating bill will be $\$216$ .