Question

With a $1200W$ toaster, how much electrical energy is needed to make a slice of toast (cooking time $1$ minute)? At $9.0cents/kW/h$, how much does this cost?

Short answer

The electrical energy needed is $0.02kW/h$, and the electricity cost is$0.18cents$

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 power consumed by the toaster is: $P=(1200W)\left(\frac{1kW}{1000W}\right)=1.2kW$.
• The cooking time of a slice of toast is: $\mathrm{\Delta }t=(1min)\left(\frac{1h}{60min}\right)=\frac{1}{60}h$.
• The cost of electricity is: Cost: $9.0cents/kW/h$ .

Calculation of the cost

The amount of energy required to slice toast is, from Equation $(1)$:

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

Substituting the value of $P$ and $\mathrm{\Delta }t$

$\begin{array}{rl}E& =(1.2kW)(\frac{1}{60}h)\\ & =0.02kW/h\end{array}$

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

$\begin{array}{rl}Total\cos t& =(0.02kW/h)\left(9.0\frac{cents}{kW/h}\right)\\ & =0.18cents\end{array}$

Therefore, the electrical energy needed is $0.02kW/h$ , and the electricity cost is$0.18cents$.