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3.06 Energy consumption of appliances

Worksheet
Conversions
1

Express the following rates in watts:

a

682 joules per second

b

1250 joules per second

c

15 kilojoules per second

d

1.9 kilojoules per second

2

Calculate how many joules are in the following. Use the fact that 1\text{ kWh}=3.6 \times 10^{6}\text{ J} and express your answer as a basic numeral.

a
4\text{ kWh}
b
104.23\text{ kWh}
c
27\text{ kWh}
d
0.81\text{ kWh}
3

Calculate how many kilojoules are in the following:

a
8\text{ kWh}
b
22\text{ kWh}
c
108.7\text{ kWh}
d
6.8\text{ kWh}
Energy consumption of appliances
4

An appliance consumes energy at a rate of 1200 \text{ W}. If it runs for 29 seconds, calculate how many joules of energy it uses.

5

5.4\text{ kWh} is used by an appliance for 10 hours. How many kilowatts is this?

6

An appliance consumes energy at a rate of 0.59\text{ kW} for 8 hours. How much energy is this in \text{kWh}?

7

An appliance consumes energy at a rate of 0.23\text{ kW}. If the appliance consumes 2.07\text{ kWh}, how long is the appliance in use?

8

Find the number of hours each appliance has been operating to the nearest hour:

a
A 1300\text{ W} microwave has a total running cost of \$586.04 over a period of time. It is using electricity that costs \$0.49\text{ per kWh} on average.
b

A 135\text{ W} computer has a total running cost of \$68.85 over a period of time. It is using electricity that costs \$0.3\text{ per kWh} on average.

9

To work out the power in kilowatts \left( \text{kW} \right) produced by a bank of solar panels we use the following formula:

\text{Power } = \dfrac{\text{Number of panels} \times \text{Power output of each panel}}{1000}

a

Calculate the power (in \text{ kW}) provided by a bank of 30 solar panels, each with a power output of 150 \text{ W}.

b

Calculate the power (in \text{ kW}) provided by a bank of 12 solar panels, each with a power output of 200 \text{ W}.

c

\text{kWh} is the measurement used to determine the size of a system of solar panels. To calculate \text{kWh}, we multiply the \text{kW} capacity of a system by the number of hours of full sunlight per day. Hence, if we estimate this to be 6 hours per day, calculate the size of the system in part (b).

10

Calculate the energy consumption for the appliances in the table below:

\text{Appliance}\text{Power (W)}\text{Time (s)}\text{Energy consumed (J)}
\text{Espresso Machine}3802400
\text{Electric Blanket}15025\,200
\text{Washing Machine}5605400
\text{Gaming Console}1207200
\text{Ceiling Fan}6514\,400
11

A washing machine is used for a total of 16 hours per month. Its monthly electricity cost is \$1.8648.

If 1\text{ kWh} costs \$0.185, how many kilowatts does the appliance use each hour?

12

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

a

How much energy (in \text{kWh}) does it use per week?

b

What is the cost of operating the iron for one year if the price of electricity is \$0.2785\text{/kWh}? Assume there are 52 weeks in a year.

13

Gwen uses a 900-watt microwave for 8 hours every day.

a

How much energy does it use:

i

Per day

ii

Per week

b

What is the cost of operating the microwave for a week if the price of electricity is \$0.2622\text{ per kWh}?

14

A microwave oven uses 0.95 kilowatts each hour. In a month, this appliance runs for 8 hours.

If electricity costs \$0.185\text{ per kWh}, what is the cost of this appliance for the month?

15

A household wants to find the cost of running their appliances in the kitchen. The appliances, the amount of watts consumed, and the amount of time they are active in a day are given in the table below:

\text{Appliance}\text{Power required (W)}\text{Time active (hours)}
\text{Toaster}11000.5
\text{Kettle}12000.6
\text{Light globe}906

The average rate for electricity is \$0.14 \text{ per kWh}. Find the average running cost of the kitchen appliances in one day.

16

Calculate the running cost for a single day use of each of the following appliances given that the average rate for electricity is \$0.12\text{ per kWh}:

a

The fridge in a house consumes 3.6\text{ kWh} of energy in a day.

b

The air conditioner in a house consumes 2.4\text{ kWh} of energy in a day.

c

An office microwave consumes energy at a rate of 1100 watts. The microwave runs for 3 hours in a day.

17

Kathleen, Jack and Aaron live at different houses and have different electricity plans. The cost of electricity for each of them is shown in the table below:

\text{House}\text{Electricity Cost (per kWh)}
\text{Kathleen}\$0.16
\text{Jack}\$0.26
\text{Aaron}\$0.17

Calculate the electricity cost to run the following appliances:

a

Kathleen's printer is operating for a total of 2 hours over a working day. It will run on 12\text{ W} during the 5-day working week.

b

Kathleen's kettle is operating for a total of 15 minutes a day over 30 days. It will run on 1608\text{ W}.

c

Jack's air conditioner is operating for a total of 840 hours. It will run on 1303 \text{ W}.

d

Jack's scanner is operating for a total of 2247 hours. It will run on 12 \text{ W}.

e

A 1500\text{ W} kettle of Aaron is operating for a total of 820 hours over a period of time.

f

A 14\text{ W} printer of Aaron is operating for a total of 2447 hours.

18

Given that there are 365 days in a year, find the running cost for each of the following for one year:

a

A fridge consumes energy at a rate of 210 watts. The fridge remains on all year. The average rate for electricity is \$0.14\text{ per kWh}.

b

A 1700-watt heater is on for 540 hours in a year, and a 700-watt fan is on for 450 hours a year. The average rate for electricity is \$0.11\text{ per kWh}.

c

A heater consumes 185\text{ kWh} of energy per year. The average cost of electricity is \$0.19\text{ per kWh}.

19

Amy is looking to purchase a new coffee machine for the office. She is deciding between 2 models that cost the same, the 1050-watt Cuppa Joe brand and the 800-watt Java Juicer brand. The coffee machines will be on for approximately 0.6 hours a day. The average rate for electricity is \$0.17 \text{ per kWh}. Assume there are 365 days in a year.

a

Calculate the yearly running cost of the Cuppa Joe brand coffee machine.

b

Calculate the yearly running cost of the Java Juicer brand coffee machine.

c

Given that both models perform the same, which brand should Amy choose?

20

Frank needs a new washing machine. He is deciding between 2 models that cost the same, the Washington brand and the Loaded brand. The washing machines both use different amounts of power depending on the selected cycle. The length and power required for each cycle are given in the tables below:

Washington Model:

Power (Watts)Time (Hours)
Wash Cycle2000.4
Spin Cycle3100.4

Loaded Model:

Power (Watts)Time (Hours)
Wash Cycle7000.2
Spin Cycle8000.025

Frank knows he performs around 60 loads of washing a year. The average rate for electricity is \$0.12 \text{ per kWh}.

a

Calculate the yearly running cost of the Washington appliance.

b

Calculate the yearly running cost of the Loaded appliance.

c

If Frank wants to save on overall costs, which brand should he choose?

21

Emma is upgrading all 9 light globes in her house to energy saving globes. Her current globes are 60 \text{ W} and the energy saving globes are 9 \text{ W}. Each globe will be used for approximately 1750 hours a year. The average rate for electricity is \$0.16 \text{ per kWh}.

a

Calculate the yearly running cost of the original light globes in the house.

b

Calculate the yearly running cost of the energy saving light globes.

c

How much will Emma save each year on lighting costs after she makes the switch to energy saving globes?

22

A television is used for 4 hours a day and consumes energy at a rate of 320 \text{ W}. The average rate for electricity is \$0.14 \text{ per kWh}. Assume that there are 365 days in a year.

a

Calculate the yearly running cost of the television.

b

To save money, the television is now to be used for only 1.5 hours a day. Calculate how much money will be saved in a year.

23

Gwen is searching for a new dishwasher for her restaurant. Her 2 options are the 2000-watt Power Clean brand for \$1000 and the 1500-watt Sparkle Sparkle brand for \$1400. The dishwasher will be used for approximately 2 hours a day. The average rate for electricity is \$0.16 \text{ per kWh}. Assume that there are 365 days in a year.

a

Calculate the yearly running cost of the Power Clean dishwasher.

b

Calculate the yearly running cost of the Sparkle Sparkle dishwasher.

c

How much would Gwen save in running costs each year in by purchasing the more expensive Sparkle Sparkle model?

d

Gwen purchases the more expensive Sparkle Sparkle brand. How long will it take for the savings in running costs to make up the extra cost of the Sparkle Sparkle dishwasher? Give your answer in years to two decimal places.

24

Harry uses his computer for 2.5 hours a day. It requires 135 \text{ W} to operate. Nadia is using a different model of computer for 12 hours a day that requires 70 watts to operate. The average rate for electricity is \$0.15 \text{ per kWh}. Assume that there are 365 days in a year.

a

Calculate the yearly running cost of Harry's computer.

b

Calculate the yearly running cost of Nadia's computer.

c

Harry purchases the other computer by selling his first. He had to spend an additional \$135 to cover the cost difference. How long will it take for the yearly energy savings to be greater than the extra cost of the new laptop? Give your answer in years to two decimal places.

25

Sophia and Neville are comparing heaters. Sophia's heater requires 610 \text{ W} and takes 1.5 hours to heat their room. Neville's heater requires 1190 \text{ W}, but it takes only 0.6 hours to heat their room. They both have the same average rate for electricity, which is \$0.13 \text{ per kWh}.

a

State whose heater is the most cost efficient in heating their room.

b

Sophia heats up the room 125 times a year and Neville heats up the room 176 times a year. Who has the cheaper yearly running cost?

26

A family received an electricity bill of \$405 in the last quarter, with electricity charged at 22.5 cents per \text{kWh}. They are considering installing a new 2.8\text{ kW} air conditioning unit and estimate that they’ll use it for 9 hours each day.

a

How many \text{ kWh} did they use in the last quarter?

b

How many\text{ kWh} will the air conditioning unit generate in the next quarter? Assume there are 90 days in a quarter.

c

How much cost would the air conditioning unit add to their next quarterly electricity bill?

27

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 loads. They find a 2-star rated dishwasher for \$320 that uses 1.9 \text{ kWh} per load and compare this to an energy saving 4-star rated dishwasher which costs \$460 and uses 1.1 \text{ kWh} per load. 1 \text{ kWh} costs 17 cents.

a

Over a one year period, how much will the family expect to save in electricity costs using the 4-star dishwasher rather than the 2-star dishwasher?

b

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

28

An office manager is comparing the price and energy consumption of televisions. They expect that over a year, they will use the television for 6 hours per day. They find a 3-star rated television for \$750 that uses 274 \text{ kWh} per year, and compare this to an energy saving 9-star rated television which costs \$1083 and uses 72 \text{ kWh} per year. 1 \text{ kWh} costs 17 cents.

a

Over a one year period, how much will they expect to save in electricity costs using the 9-star television rather than the 3-star television?

b

How many whole years will it take for the electricity savings to offset the difference in purchase price of the televisions?

29

Sophia’s family just installed a 25 \text{ W} Compact Fluorescent Lamp (CFL) bulb in their kitchen. It gives off the equivalent amount of light of a 100 \text{ W} incandescent bulb. They use the light for 5 hours each day. Peter's family has a 100 \text{ W} incandescent bulb in their kitchen, and use it from 6 pm to 10 pm each day. 1 \text{ kWh} costs 20.9 cents.

a

Find how many kilowatt hours the CFL uses over the time Sophia’s family uses it each day.

b

Find how many kilowatt hours the incandescent bulb uses over the time Peter’s family uses it.

c

Which bulb uses more power?

d

How much does the CFL cost Sophia’s family each day? Do not round your answer.

e

How much does the incandescent bulb cost Peter's family each day? Do not round your answer.

f

Over a one year period (365 days), calculate the difference in the bill that the two families pay for their kitchen lighting.

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MS11-3

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

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