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?

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{aligned}E &= \left( {{\rm{kW}}} \right) \times \left( {\rm{h}} \right)\\ &= {\rm{kW}} \cdot {\rm{h}} \end{aligned}

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{aligned}E &= \left( {15.0{\rm{ kW}}} \right) \times \left( {3.00{\rm{ h per day}}} \right) \times \left( {30.0{\rm{ day}}} \right)\\ &= 1350{\rm{ kW}} \cdot {\rm{h}} \end{aligned}

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

\begin{aligned}{\rm{Cost}} &= \left( {\$ 0.100{\rm{ per kW}} \cdot {\rm{h}}} \right) \times \left( {1350{\rm{ kW}} \cdot {\rm{h}}} \right)\\ &= \$ 148.5 \end{aligned}

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