Question

A large household air conditioner may consume 15.0 kW of power. What is the cost of operating this air conditioner 3.00 h per day for 30.0 d if the cost of electricity is $0.110 per kW⋅h?

Short answer

The cost of operating air conditioner is $148.5.

Step-by-step solution

Power

The rate at which energy is expended is defined as power.

The energy consumption is given as,

E=PT

Here,P is the power rating of the appliances and T is the time of operation.

The larger unit of power is kilowatt (kW) and that of time is hour (h). Therefore,

$$\begin{array}{rl}E& =\left(\mathrm{k}\mathrm{W}\right)\times \left(\mathrm{h}\right)\\ & =\mathrm{k}\mathrm{W}\cdot \mathrm{h}\end{array}$$

As a result, the commercial unit of the energy consumption is kilowatt-hour.

When an air conditioner rated 15.0 kW is operated of 3.00 h per day for 30.0 day. The energy consumed by the air conditioner in 30.0 day is,

$$\begin{array}{rl}E& =\left(15.0\mathrm{k}\mathrm{W}\right)\times \left(3.00\mathrm{h}\mathrm{p}\mathrm{e}\mathrm{r}\mathrm{d}\mathrm{a}\mathrm{y}\right)\times \left(30.0\mathrm{d}\mathrm{a}\mathrm{y}\right)\\ & =1350\mathrm{k}\mathrm{W}\cdot \mathrm{h}\end{array}$$

Cost of electric bill

If the electric bill is charged for $0.110 per kW.h. Therefore, the cost of the electric bill is,

$$\begin{array}{rl}\mathrm{C}\mathrm{o}\mathrm{s}\mathrm{t}& =\left(\mathrm{\$}0.100\mathrm{p}\mathrm{e}\mathrm{r}\mathrm{k}\mathrm{W}\cdot \mathrm{h}\right)\times \left(1350\mathrm{k}\mathrm{W}\cdot \mathrm{h}\right)\\ & =\mathrm{\$}148.5\end{array}$$

Therefore, the required cost of operating air conditioner is $ 148.5.