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5F

Energy at home and in food

Power in watts, energy in kilowatt-hours, the running cost of appliances, energy rating labels, and food energy in kilojoules and Calories.

Your power bill and a nutrition panel are measuring the same thing: energy. One counts what your house uses in kilowatt-hours, the other counts what your body takes in as kilojoules. Being able to read both is everyday maths that saves real money.

Power and energy

Power is how fast an appliance uses energy, measured in watts (W). A $2200$ W kettle uses energy much faster than a $10$ W phone charger. $1$ kilowatt (kW) $= 1000$ W.

Energy is how much is used in total, which depends on the power and how long it runs. Electricity companies measure it in kilowatt-hours (kWh): one kilowatt running for one hour.

Electrical energy
$$\text{Energy (kWh)} = \text{power (kW)} \times \text{time (h)} \qquad 1 \text{ kWh} = 3.6 \text{ MJ}$$

Running costs

Your bill charges a price per kWh, called the usage rate or tariff, plus a fixed daily supply charge. Usage rates change every year and between retailers. The examples here use $35$ cents per kWh, which is in the right range for NSW households, but always use the rate in the question.

Example 1●

A $2400$ W fan heater runs for $3$ hours a night for $30$ nights. Electricity costs $35$ c/kWh. Find the cost.

$2400$ W $= 2.4$ kW
Convert watts to kilowatts.
$2.4 \times 3 \times 30 = 216$ kWh
Energy = power × time, using the total hours.
$216 \times \$0.35 = \$75.60$
Multiply by the price per kWh, converting cents to dollars.
InteractiveHousehold energy meter
Try this
  • Which appliance costs the most per day? Is it the one with the highest wattage, or the one that runs longest?
  • Turn everything off except the phone charger at $3$ h a day. How many years would it take to cost $\$10$?
  • Turn the clothes dryer on for $1$ hour. Compare its daily cost with drying on the line, which is free.
  • Move the electricity price from $30$ c to $45$ c. By how much does the quarterly bill change?

Energy rating labels

Fridges, washing machines, TVs and air conditioners sold in Australia carry an Energy Rating Label. More stars means more efficient, and the big number in the middle tells you the energy used per year in kWh under standard testing. That number is the one to use in calculations.

Example 2●●

Fridge A is labelled $350$ kWh per year and costs $\$1290$. Fridge B is labelled $500$ kWh per year and costs $\$1150$. Electricity is $35$ c/kWh. Over a $10$ year life, which is cheaper overall?

$500 - 350 = 150$ kWh per year
Find the extra energy fridge B uses each year.
$150 \times \$0.35 = \$52.50$ per year
Turn that energy into dollars.
$\$52.50 \times 10 = \$525$
Over ten years the extra running cost adds up.
Fridge A is about $\$525 - \$140 = \$385$ cheaper over its life.
B costs 140 dollars less to buy but 525 dollars more to run.

Energy in food

Food energy is measured in kilojoules (kJ). Every packaged food in Australia has a nutrition information panel with the energy per serve and per $100$ g. The per $100$ g column is the one to use when comparing two products, because serve sizes are chosen by the company.

Many apps and overseas labels use Calories. A food Calorie (capital C) is really a kilocalorie, and $1$ Cal $= 4.184$ kJ. Some textbooks write "calorie" with a small c here, but strictly that is a unit a thousand times smaller.

Food energy
$$1 \text{ Cal} = 4.184 \text{ kJ}$$
Example 3●●

A muesli bar has $450$ kJ. Convert this to Calories, and find how long you would need to jog to use it up if jogging uses about $2000$ kJ per hour.

$450 \div 4.184 \approx 108$ Cal
kJ to Cal: divide by 4.184.
$\dfrac{450}{2000} = 0.225$ h
What fraction of an hour of jogging is 450 kJ?
$0.225 \times 60 = 13.5$ min
Hours to minutes: multiply by 60.

Daily energy needs depend on age, size and how active you are. A typical figure for a teenager is somewhere around $8000$ to $12\,000$ kJ a day. Exercise figures like "$2000$ kJ per hour" are averages too, so treat answers from them as estimates.

Your turn

A phone battery holds about $15$ Wh. At $35$ c/kWh, how much does a full charge cost?

Show the working

$15$ Wh $= 0.015$ kWh. Cost $= 0.015 \times 35 = 0.525$ cents, about half a cent. A year of daily charging is under $\$2$.

Flashcards
Energy in kWh
Power in kW $\times$ time in hours
$1$ kWh in megajoules
$3.6$ MJ
$1$ food Calorie
$4.184$ kJ
Practice

  1. A kettle is rated at $1500$ W. What is its power in kW?

  2. A $2000$ W air conditioner runs for $5$ hours. How many kWh does it use?

  3. Electricity costs $32$ c/kWh. What does $10$ kWh cost, in dollars?

  4. A $60$ W TV is on for $4$ hours a day for a $91$ day quarter. How many kWh does it use?

  5. The kilowatt-hour is a unit of:

  6. Convert $800$ kJ to Calories, correct to one decimal place.

  7. Sam needs about $9000$ kJ a day. Lunch was $2600$ kJ. What percentage of the daily need is that, to the nearest whole number?

  8. How many megajoules are in $5$ kWh?

  9. Exam style: A $2.5$ kW clothes dryer runs for $1.5$ hours, three times a week, for $52$ weeks. Electricity costs $34$ c/kWh. Find the yearly cost in dollars.

  10. Exam style: A family replaces eight $60$ W globes with eight $9$ W LED globes. The lights are on $5$ hours a day. At $35$ c/kWh, how much do they save in a year (365 days), in dollars?

Formula sheet