Question

The average television is said to be on $6hours$ per day. Estimate the yearly cost of electricity to operate $100million$ TVs, assuming their power consumption averages $150W$and the cost of electricity averages $12.0cents/kW\cdot h$.

Short answer

The yearly cost of electricity is $\mathrm{\$}3.94B/year$.

Step-by-step solution

Definition of Power

The power of a process is the amount of some type of energy converted into a different type divided by the time interval$\mathrm{\Delta }t$in which the process occurred:

$P=\frac{\mathrm{\Delta }E}{\mathrm{\Delta }t}......(1)$

The SI unit of power is the watt$(W)$.

$1$ Watt is$1$joule/second$(1W=1J/s)$.

The given data

• The time of operation of the average television is: $\mathrm{\Delta }t=6h/day$.
• The average power consumption per TV is:$P=150W/TV$.
• The average cost of electricity is: Cost is: $12.0cents/kW\cdot h$.

Calculation of the energy consumed

The amount of energy consumed by $100million$ TVs that run $6$ hours a day each year is found from Equation $(1)$:

$E=P\mathrm{\Delta }t$

Substituting the values:

$\begin{array}{r}E=(150W/TV)\left(100\times {10}^{6}TV\right)\left(\frac{6h}{day}\right)\left(\frac{365days}{1year}\right)\\ =3.285\times {10}^{13}W/h/year\\ =3.285\times {10}^{10}kW/h/year\end{array}$

The energy consumed $3.285\times {10}^{10}kW/h/year$.

Calculation of energy cost

The cost of energy is found by multiplying $E$ by the cost of each $1kW/h$:

$\begin{array}{r}\mathrm{Cos}t=\left(3.285\times {10}^{10}kW/h/year\right)(12.0cents/kW/h)\\ =3.942\times {10}^{11}cents/year\\ =\left(3.942\times {10}^{11}cents/year\right)\left(\frac{\mathrm{\$}1}{100cents}\right)\left(\frac{\mathrm{\$}1B}{\mathrm{\$}{10}^9}\right)\\ =\mathrm{\$}3.94B/year\end{array}$

Therefore, the energy cost is $\mathrm{\$}3.94B/year$.