NSW Mathematics Standard 11 - 2020 Edition
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3.06 Energy consumption of appliances
Lesson

Electricity is a form of energy used in homes and businesses for running various appliances and machines. 

Every appliance has a power rating, which indicates the rate at which it consumes or generates energy. The power rating is measured in watts (W), where $1$1 watt is equal to $1$1 joule per second. A kilowatt (kW) is simply $1000$1000 watts. An electric kettle, for example may have a power rating of $1800$1800 W, or $1.8$1.8 kW. This is the amount of electricity the kettle would consume during one hour of operation.

Energy consumption in the home is generally measured in kilowatt hours (kWh). One kWh is equal to $3.6\times10^6$3.6×106 joules of energy, or $3.6$3.6 megajoules (MJ).

 

Practice Question

question 1

Use the fact that $1$1 kWh = $3.6\times10^6$3.6×106 J to calculate how many joules $104.23$104.23 kWh is equal to.

  1. Express your answer as a basic numeral.

 

Energy consumption of appliances

Energy consumption is the amount of energy consumed per unit of time. For appliances that use electricity, we measure their energy consumption in kilowatt hours (kWh). We can calculate the energy consumption of an appliance over time by using:

Energy consumption (kWh) $=$= power (kW) $\times$× time (h)

Electricity suppliers usually charge households and businesses for the electricity they use, in cents per kWh.

Larger amounts of electrical energy consumption could be expressed in megawatt-hours (MWh).

 

Worked example

Belle has a $80$80-watt television that she watches $4$4 hours every day. 

(a) How many energy (in kWh) does the television use per day?

Think: Convert from watts to kilowatts, by dividing by $1000$1000, then multiply by the number of hours the appliance is used each day.

Do:

Daily electricity consumption $=$= $\frac{80}{1000}\times4$801000×4
  $=$= $0.08\times4$0.08×4
  $=$= $0.32$0.32 kWh

 

(b) How much will the television cost to operate each day if electricity is charged at $\$0.18$$0.18 per kWh?

Think: Multiply the usage by the rate.

Do:

Daily cost of running the TV $=$= $0.32\times0.18$0.32×0.18
  $=$= $\$0.0576$$0.0576

 

Therefore it costs approximately $5.8$5.8 cents to operate the television each day.

 

Practice Questions

Question 2

Valentina uses a $550$550-watt iron for $8$8 hours every week.

  1. How much energy (in kWh) does it use per week?

  2. What is the cost of operating the iron for one year if the price of electricity is $\$0.2785$$0.2785/kWh, correct to the nearest cent?

    Assume there are $52$52 weeks in a year.

Question 3

Based on the data supplied, if an electricity company charges $\$0.245$$0.245 per kWh, what would a typical household's electricity bill cost for the entire season of Autumn?

  1. Round your answer to the nearest cent.

 

 

Energy rating of appliances

We rely on electrical energy for many of our daily activities. This can lead to high electricity bills, but also high carbon dioxide emissions. 

One way we can reduce our energy consumption is to use more energy efficient appliances. In Australia an energy rating label is attached to appliances like refrigerators, televisions, dishwashers, and air conditioners.

A numerical value on the label indicates how much energy the appliance might typically use in a year, while a star rating indicates the energy efficiency of the appliance. Energy rating labels allow consumers to compare different brands and models across similar products. 

                                   

The lower the number in the red box, the less it will cost to run. The higher the number of stars, the more energy efficient the appliance is.

 

Practice Questions

Question 4

A heater consumes $185$185 kWh of energy per year. Calculate the cost of operating the heater for a year if the average cost of electricity is $\$0.19$$0.19 per kWh.

Question 5

A family is comparing the price and energy consumption of dishwashers in a store. They expect that over a year they will use the dishwasher for $320$320 loads. They find a $2$2-star rated dishwasher for $\$320$$320 that uses $1.9$1.9 kWh per load, and compare this to an energy saving $4$4-star rated dishwasher which costs $\$460$$460 and uses $1.1$1.1 kWh per load.

Use the fact that $1$1 kWh costs $17$17 cents to answer the following questions.

  1. Over a one year period, how much will they expect to save in electricity costs using the $4$4-star dishwasher rather than the $2$2-star dishwasher? Round your answer to the nearest cent.

  2. Will the electricity saving in the first year offset the difference in purchase price of the dishwashers?

    Yes

    A

    No

    B

    Yes

    A

    No

    B

Outcomes

MS11-3

solves problems involving quantity measurement, including accuracy and the choice of relevant units

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