Chapter 8 of 8

All 8 chapters
  1. 1Calculating energy stores, readunderstood
  2. 2Springs and elastic energy, readunderstood
  3. 3Work done, readunderstood
  4. 4Power, readunderstood
  5. 5Efficiency, readunderstood
  6. 6Specific heat capacity, readunderstood
  7. 7Energy resources, readunderstood
  8. 8Energy at home, readunderstood

S4.9.8 Chapter 8

Energy at home

A 1 kW iron is used for 2 hours. How much energy does it use?

Your guess

Pick one before you read on. It is fine to be wrong.

Your guess

  • You picked A. Read on. At the end, the chapter comes back to your guess.

  • You picked B. Read on. At the end, the chapter comes back to your guess.

  • You picked C. Read on. At the end, the chapter comes back to your guess.

  • You picked D. Read on. At the end, the chapter comes back to your guess.

By the end you can

  • Calculate the cost of running an appliance from its power and time
  • Compare the yearly cost of a filament lamp and an LED lamp

A home pays for energy. The joule is far too small for the bill. A lamp that is on for one hour already uses tens of thousands of joules. So the bill counts energy in a bigger unit.

A kilowatt hour (kWh) is the energy used by a 1 kW appliance running for 1 hour. 1 kWh = 1 kW × 1 h = 1 000 W × 3 600 s = 3 600 000 J, which is 3.6 MJ.

energy in kWh = power in kW × time in hours. The cost is the energy in kWh times the price for each kWh.

Prices differ from place to place. In this chapter the price is 10 coins for each kWh. Many bills call one kWh a "unit", so a price for each unit is a price for each kWh.

A table of the units used at home with the columns Quantity and Unit. Power is in kW. Time is in h. Energy is in kWh.QuantityUnitpowerkWtimehenergykWh
Use kW and h together, and the answer comes out in kWh.

Worked example

A 2 kW electric heater runs for 3 hours. The price is 10 coins for each kWh. How much energy does it use, and what does it cost?

  1. energy = power × time.
  2. E = 2 × 3 = 6 kWh.
  3. cost = 6 × 10 = 60 coins.

Answer: 6 kWh, which costs 60 coins

A meter on the wall counts the kWh used. Read it at the start and at the end. The difference is the energy used. The last dial, shaded here, shows tenths of a kWh.

Two electricity meter counters, one above the other. The first is labelled before and shows the digits 0, 2, 3, 0, 4 and then 5 tenths, that is 2 304.5 kWh. The second is labelled after and shows the digits 0, 2, 3, 1, 0 and then 5 tenths, that is 2 310.5 kWh. Each counter is labelled kWh.before023045kWhafter023105kWh
The meter before and after the heater ran. 2 310.5 − 2 304.5 = 6 kWh.

Most appliances are rated in watts. Change watts to kilowatts by dividing by 1 000. Change minutes to hours by dividing by 60. Forget either change and the answer is wrong by a large factor.

Worked example

A 500 W iron is used for 90 minutes. How much energy does it use, in kWh?

  1. energy in kWh = power in kW × time in h.
  2. 500 W = 0.5 kW, and 90 minutes = 90 ÷ 60 = 1.5 h.
  3. E = 0.5 × 1.5 = 0.75 kWh.

Answer: 0.75 kWh

Do not mix up the units. A kilowatt is a rate of using energy. A kilowatt hour is an amount of energy. A 2 kW heater has a power of 2 kW. It uses 2 kWh in each hour.

More power does not always mean more cost. The cost depends on the power and the time. A strong appliance used for a short time can cost less than a weak one left on for hours.

A bar chart of energy used. The axis is labelled energy in kWh, with a scale from 0 to 0.5 in steps of 0.25. The bar for kettle 0.2 kWh, a 2 kW kettle for 6 minutes, reaches 0.2. The bar for TV 0.5 kWh, a 100 W television for 5 hours, reaches 0.5.00.250.5kettle 0.2 kWhTV 0.5 kWhenergy in kWh
The kettle runs for 6 minutes and the television for 5 hours. The kettle has twenty times the power, yet uses less energy, because it runs for a short time.

Devices left on standby still use power all day. A device on standby at 5 W uses 0.005 kW × 24 h = 0.12 kWh in a day. Newer devices often use less than 1 W on standby. A few of them still add up over a year.

Now compare two lamps that give the same light. A filament lamp uses 50 W. An LED lamp uses 10 W. This matches Chapter 5. A typical filament lamp turns about 6% of its energy into light. A typical LED lamp turns about 30%. So both give about 3 W of light. Real lamps differ. A filament lamp turns only a few percent of its energy into light. An LED lamp turns about a third.

Worked example

A filament lamp uses 50 W and an LED lamp uses 10 W. They give the same light. Each is on for 1 000 hours in a year. The price is 10 coins for each kWh. How much more does the filament lamp cost to run for the year?

  1. energy in kWh = power in kW × time in h.
  2. Filament: 0.05 kW × 1 000 h = 50 kWh, which costs 50 × 10 = 500 coins.
  3. LED: 0.01 kW × 1 000 h = 10 kWh, which costs 10 × 10 = 100 coins.
  4. The filament lamp costs 500 − 100 = 400 coins more.

Answer: 400 coins

A bar chart of the energy used by two lamps in a year. The axis is labelled energy in kWh, with a scale from 0 to 50 in steps of 10. The bar for the filament lamp reaches 50. The bar for the LED lamp reaches 10.01020304050filament lampLED lampenergy in kWh
Both lamps give the same light for 1 000 hours. The filament lamp uses five times the energy.

An LED lamp costs more to buy. So a fair comparison also asks how long the yearly saving takes to pay back the higher price. The saving here is large, so the LED lamp pays back its extra price in a short time.

A wrong idea many people have

A kilowatt hour is a unit of power, kilowatts for each hour.

Why it feels right: Power units such as watts already mean "for each second", so "for each hour" sounds like a power too.

The test that breaks it: Multiply: kW × h. A 1 kW iron running for 2 hours gives 1 × 2 = 2 kWh. That is a power times a time, which is an energy, like a W times a s gives joules.

What is true: A kilowatt hour is a unit of energy: the energy used by 1 kW running for 1 hour. It equals 3.6 MJ.

Try it

What does your home use in a day?

You need: paper and a pencil, three electrical appliances to look at, such as a kettle, a lamp and a television.

Be safe: Only read the labels. Do not open any appliance, and do not touch plugs or sockets with wet hands. Leave a hot kettle alone until it cools.

  1. Look for the label on each appliance. It is on the back or the bottom. Write down its power in W or kW.
  2. Change each power to kW. Divide a W by 1 000.
  3. Estimate for how many hours a day each one is on. A kettle may be on for only 6 minutes, which is 0.1 h.
  4. For each, work out the energy in kWh: power in kW × hours.
  5. Which appliance uses the most energy in a day? Is it the one with the highest power?

What you will see: In the example, the kettle has by far the highest power but is on for the shortest time. The television uses the most energy in the day. The answer depends on the power and the time together.

If you cannot try it, this is what happens.
A table of an example day with the columns Item, Power, Hours and kWh. Kettle: 2 kW, 0.1 hours, 0.2 kWh. Lamp: 0.01 kW, 5 hours, 0.05 kWh. TV: 0.1 kW, 6 hours, 0.6 kWh.ItemPowerHourskWhkettle2 kW0.10.2lamp0.01 kW50.05TV0.1 kW60.6

Key words

kilowatt hour
a unit of energy, written kWh. It is the energy used by a 1 kW appliance in 1 hour, which is 3.6 MJ.
power rating
the power an appliance uses when it runs, printed on its label in W or kW.

Back to your guess

The answer is D: 2 kWh

Energy in kWh is power in kW times time in hours: 1 kW × 2 h = 2 kWh. Adding the numbers gives 3, and dividing gives 0.5.

Check yourself

Try each one before you look. A wrong answer tells you where to go next.

  1. What is a kilowatt hour?

    Tap your answer.

    1. Yes, that is right. A kilowatt hour is power times time: 1 kW for 1 h. It is a unit of energy.

    2. Not this one. A kilowatt is already a rate, joules each second. A kilowatt hour multiplies it by a time, so it is an amount of energy. Try another.

    3. Not this one. It is a unit of energy, not of time. Try another.

    4. Not this one. A thousand watts is one kilowatt, which is a power. A kilowatt hour is an amount of energy. Go to S4.9.4. Try another.

    See the answer

    The energy used by a one kilowatt appliance in one hour.

    A kilowatt hour is power times time: 1 kW for 1 h. It is a unit of energy.

    • If you chose B: A kilowatt is already a rate, joules each second. A kilowatt hour multiplies it by a time, so it is an amount of energy.
    • If you chose C: It is a unit of energy, not of time.
    • If you chose D: A thousand watts is one kilowatt, which is a power. A kilowatt hour is an amount of energy. Go to S4.9.4.

  2. A 3 kW heater runs for 4 hours. How much energy does it use?

    Tap your answer.

    1. Not this one. You added 3 and 4. Energy is power multiplied by time. Try another.

    2. Yes, that is right. energy = power × time = 3 kW × 4 h = 12 kWh.

    3. Not this one. You divided 3 by 4. Energy is power multiplied by time. Try another.

    4. Not this one. You changed the power to watts but kept kWh. Use kW with hours to get kWh. Try another.

    See the answer

    12 kWh

    energy = power × time = 3 kW × 4 h = 12 kWh.

    • If you chose A: You added 3 and 4. Energy is power multiplied by time.
    • If you chose C: You divided 3 by 4. Energy is power multiplied by time.
    • If you chose D: You changed the power to watts but kept kWh. Use kW with hours to get kWh.

  3. An 80 W lamp is on for 5 hours. How much energy does it use, in kWh?

    Tap your answer.

    1. Not this one. You did not change 80 W to kW. 80 W is 0.08 kW. Go to S4.9.4. Try another.

    2. Not this one. You divided 80 by 5. Energy is power in kW multiplied by time in hours. Try another.

    3. Not this one. You added 80 and 5. Energy is power multiplied by time, and the power must be in kW. Try another.

    4. Yes, that is right. 80 W = 0.08 kW. energy = 0.08 × 5 = 0.4 kWh.

    See the answer

    0.4 kWh

    80 W = 0.08 kW. energy = 0.08 × 5 = 0.4 kWh.

    • If you chose A: You did not change 80 W to kW. 80 W is 0.08 kW. Go to S4.9.4.
    • If you chose B: You divided 80 by 5. Energy is power in kW multiplied by time in hours.
    • If you chose C: You added 80 and 5. Energy is power multiplied by time, and the power must be in kW.

  4. An appliance uses 3.5 kWh. The price is 10 coins for each kWh. What does it cost?

    Tap your answer.

    1. Not this one. You divided by 10. The cost is the energy multiplied by the price. Try another.

    2. Not this one. You added the price. The cost is the energy multiplied by the price. Try another.

    3. Yes, that is right. cost = energy × price = 3.5 × 10 = 35 coins.

    4. Not this one. You divided the price by the energy. The cost is the energy multiplied by the price. Try another.

    See the answer

    35 coins

    cost = energy × price = 3.5 × 10 = 35 coins.

    • If you chose A: You divided by 10. The cost is the energy multiplied by the price.
    • If you chose B: You added the price. The cost is the energy multiplied by the price.
    • If you chose D: You divided the price by the energy. The cost is the energy multiplied by the price.

  5. A 1.2 kW hairdryer is used for 15 minutes. How much energy does it use, in kWh?

    Tap your answer.

    1. Yes, that is right. 15 minutes = 15 ÷ 60 = 0.25 h. energy = 1.2 × 0.25 = 0.3 kWh.

    2. Not this one. You used 15 as if it were hours. Change 15 minutes to 0.25 h first. Go to M2.6.7. Try another.

    3. Not this one. You divided 1.2 by 0.25, which is upside down. Energy is power multiplied by time. Try another.

    4. Not this one. You added 1.2 and 15. Energy is power multiplied by time, with the time in hours. Try another.

    See the answer

    0.3 kWh

    15 minutes = 15 ÷ 60 = 0.25 h. energy = 1.2 × 0.25 = 0.3 kWh.

    • If you chose B: You used 15 as if it were hours. Change 15 minutes to 0.25 h first. Go to M2.6.7.
    • If you chose C: You divided 1.2 by 0.25, which is upside down. Energy is power multiplied by time.
    • If you chose D: You added 1.2 and 15. Energy is power multiplied by time, with the time in hours.

  6. A meter was read in the morning and again in the evening. How much energy was used between the readings, in kWh?

    Two electricity meter counters, one above the other. The first is labelled morning and shows the digits 0, 4, 1, 1, 8 and then 2 tenths. The second is labelled evening and shows the digits 0, 4, 1, 2, 5 and then 7 tenths. Each counter is labelled kWh.morning041182kWhevening041257kWh
    Tap your answer.

    1. Not this one. You added the two readings. The energy used is the difference between them. Try another.

    2. Not this one. You ignored the tenths on the last dial. 4 125.7 − 4 118.2 = 7.5. Try another.

    3. Not this one. That is the reading in the evening, not the energy used. Take away the morning reading. Try another.

    4. Yes, that is right. The readings are 4 118.2 kWh and 4 125.7 kWh. The energy used is 4 125.7 − 4 118.2 = 7.5 kWh.

    See the answer

    7.5 kWh

    The readings are 4 118.2 kWh and 4 125.7 kWh. The energy used is 4 125.7 − 4 118.2 = 7.5 kWh.

    • If you chose A: You added the two readings. The energy used is the difference between them.
    • If you chose B: You ignored the tenths on the last dial. 4 125.7 − 4 118.2 = 7.5.
    • If you chose C: That is the reading in the evening, not the energy used. Take away the morning reading.

  7. Why does an LED lamp cost less to run than a filament lamp that gives the same light for the same hours?

    Tap your answer.

    1. Not this one. The question says both give the same light. The difference is in the power each needs. Try another.

    2. Yes, that is right. An LED lamp is more efficient. It gives the same light with a smaller power, so it uses fewer kWh in the same time.

    3. Not this one. Every lamp needs energy for its light. The LED needs less of it. Try another.

    4. Not this one. The price depends on the supplier, not on the lamp. The LED lamp uses fewer kWh. Try another.

    See the answer

    It needs less power for the same light, because it wastes less energy as heat.

    An LED lamp is more efficient. It gives the same light with a smaller power, so it uses fewer kWh in the same time.

    • If you chose A: The question says both give the same light. The difference is in the power each needs.
    • If you chose C: Every lamp needs energy for its light. The LED needs less of it.
    • If you chose D: The price depends on the supplier, not on the lamp. The LED lamp uses fewer kWh.

  8. A 60 W filament lamp and a 12 W LED lamp give the same light. Each is on for 1 000 hours in a year. The price is 10 coins for each kWh. How much more does the filament lamp cost for the year?

    Tap your answer.

    1. Not this one. You took 12 kWh from 60 kWh but did not multiply by the price. The cost is the energy times 10. Try another.

    2. Yes, that is right. Filament: 0.06 kW × 1 000 h = 60 kWh, which costs 60 × 10 = 600 coins. LED: 0.012 kW × 1 000 h = 12 kWh, which costs 12 × 10 = 120 coins. The difference is 600 − 120 = 480 coins.

    3. Not this one. That is the cost of the filament lamp alone. The question asks how much more it costs than the LED lamp. Try another.

    4. Not this one. You added the two costs. To find how much more, take the LED cost away from the filament cost. Try another.

    See the answer

    480 coins

    Filament: 0.06 kW × 1 000 h = 60 kWh, which costs 60 × 10 = 600 coins. LED: 0.012 kW × 1 000 h = 12 kWh, which costs 12 × 10 = 120 coins. The difference is 600 − 120 = 480 coins.

    • If you chose A: You took 12 kWh from 60 kWh but did not multiply by the price. The cost is the energy times 10.
    • If you chose C: That is the cost of the filament lamp alone. The question asks how much more it costs than the LED lamp.
    • If you chose D: You added the two costs. To find how much more, take the LED cost away from the filament cost.

  9. From an earlier chapter

    A solar panel delivers 100 W for 3 minutes. How much energy does it deliver?

    Tap your answer.

    1. Not this one. You used 3 as if it were seconds. Change 3 minutes to 180 s first. Go to S4.9.7. Try another.

    2. Not this one. You used 30 s for 3 minutes. 3 minutes is 3 × 60 = 180 s. Go to S4.9.7. Try another.

    3. Yes, that is right. 3 minutes = 180 s. E = P × t = 100 × 180 = 18 000 J = 18 kJ.

    See the answer

    18 kJ

    3 minutes = 180 s. E = P × t = 100 × 180 = 18 000 J = 18 kJ.

    • If you chose A: You used 3 as if it were seconds. Change 3 minutes to 180 s first. Go to S4.9.7.
    • If you chose B: You used 30 s for 3 minutes. 3 minutes is 3 × 60 = 180 s. Go to S4.9.7.

  10. A 2.5 kW heater runs for 2 hours. The price is 10 coins for each kWh. What does it cost?

    See the answer

    50 coins

    energy = 2.5 × 2 = 5 kWh. cost = 5 × 10 = 50 coins.

  11. A 60 W lamp is on for 4 hours. How much energy does it use, in kWh?

    See the answer

    0.24 kWh

    60 W = 0.06 kW. energy = 0.06 × 4 = 0.24 kWh.

  12. A 25 W lamp is on for 1 000 hours in a year. The price is 10 coins for each kWh. What does it cost for the year?

    See the answer

    250 coins

    25 W = 0.025 kW. energy = 0.025 × 1 000 = 25 kWh. cost = 25 × 10 = 250 coins.

Keep it

Copy this into your exercise book.

E (kWh) = P (kW) × t (h). W to kW: ÷ 1 000. Minutes to hours: ÷ 60. Cost = kWh × price. 1 kWh = 3.6 MJ. LED lamp: same light, less power, lower cost.

Draw: A meter before and after, with the difference in kWh, and E = P × t beside it.

Reading with a child? A short page for the adult: what this chapter teaches and three questions to ask.

No internet tomorrow? Save the whole book as one file (758 KB). It opens on any phone.