Household energy & energy audits

What you will learn

the units of electrical energy: watts, kilowatts, kilowatt-hours,
how to calculate the energy used by an appliance,
how to read an electricity bill and estimate the cost of running a device,
how energy rating labels compare appliances,
how to plan and carry out a simple home energy audit.

Worked example 0 Real-world example: cost of running a heater

A $2000$ W electric heater is left on for $4$ hours each evening during winter ( $90$ days). Electricity costs $0.30 per kWh. Estimate the total cost for winter.

Convert to kilowatts: $2000$ W $= 2$ kW.
Energy per evening: $2 \text{ kW} \times 4 \text{ h} = 8$ kWh.
Energy for winter: $8 \times 90 = 720$ kWh.
Cost: $720 \times 0.30 = 216$ dollars.

Key idea: one high-power appliance used every day dominates a whole bill. The family could consider a more efficient heater or warmer clothing.

1. Power and energy — watts and kilowatt-hours

Power is how fast energy is used. Measured in watts (W) or kilowatts (kW). $1$ kW $= 1000$ W.
Energy used is power $\times$ time. Electricity companies measure energy in kilowatt-hours (kWh).

Energy used and cost

Energy (kWh)

E \text{ (kWh)} = P \text{ (kW)} \times t \text{ (h)}.

Cost

\text{cost} = E \times \text{price per kWh}.

Worked example 1 Energy for a fridge

A fridge has a power rating of $150$ W and runs $24$ hours a day. Find the daily energy use in kWh.

Convert to kW: $150$ W $= 0.15$ kW.
Energy: $E = 0.15 \times 24 = 3.6$ kWh.
If electricity costs $0.30/kWh, daily cost $= 3.6 \times 0.30 = 1.08$ dollars.

Worked example 2 Cost of a kettle boil

A $2.4$ kW kettle boils for $3$ minutes. At $0.30/kWh, find the cost of one boil.

Time in hours: $3$ min $= 0.05$ h.
Energy: $E = 2.4 \times 0.05 = 0.12$ kWh.
Cost: $0.12 \times 0.30 = 0.036$ dollars $\approx 3.6$ cents.

2. Reading an electricity bill

A typical bill contains:

Meter reading start / end — the kWh counter at the start and end of the billing period.
Usage (kWh) — the difference, i.e. what was actually used.
Tariff — price per kWh (sometimes different for peak / off-peak / shoulder).
Supply charge — a fixed daily cost for being connected.
Total cost — usage charge + supply charge + GST.

Worked example 3 Simple bill calculation

A household reads $24\,510$ kWh at the start of the quarter and $25\,360$ kWh at the end. Tariff is $0.28/kWh; the daily supply charge is $1.20 for $90$ days.

Usage $= 25\,360 - 24\,510 = 850$ kWh.
Usage cost $= 850 \times 0.28 = 238$ dollars.
Supply charge $= 90 \times 1.20 = 108$ dollars.
Subtotal $= 238 + 108 = 346$ dollars.
Adding $10\%$ GST: $346 \times 1.10 = 380.60$ dollars.

3. Energy rating labels

Australian appliances carry a star rating (1 to 10 stars) comparing their efficiency to similar models. More stars = less electricity for the same job.

The label also prints an annual energy use (kWh/year) number. This is what you multiply by the tariff to estimate the running cost.

Worked example 4 Comparing fridges

Fridge A is rated $320$ kWh/year, fridge B is rated $480$ kWh/year. At $0.30/kWh, how much more does fridge B cost to run over 10 years?

Annual difference: $480 - 320 = 160$ kWh.
Annual cost difference: $160 \times 0.30 = 48$ dollars.
Over $10$ years: $48 \times 10 = 480$ dollars.

Key idea: a fridge lives in your home for a decade. A cheaper “label price” can easily be wiped out by higher running cost.

4. Building design, season and climate

How much energy a home uses depends on more than the appliances plugged in:

Insulation — roof, wall and floor insulation cut heating and cooling losses.
Orientation — north-facing windows (in Australia) let in winter sun for free heat.
Shading — eaves and trees block summer sun.
Windows — double glazing dramatically reduces heat loss.
Climate — a house in Darwin (tropical) uses more for cooling; one in Hobart more for heating.
Season — heating and cooling dominate winter/summer, while lighting and appliances are roughly constant.

5. The energy audit

An energy audit is a systematic check of where energy is being used and where it is wasted. Simple steps for a classroom or household audit:

List major appliances. For each, note the power rating (often on a sticker).
Estimate daily use (hours/day).
Calculate daily and annual kWh ( $P \times t \times 365$ ).
Rank the biggest users.
Look for waste: standby power, lights left on, old appliances, draughts.
Recommend actions: swap incandescents for LEDs, turn off at the wall, add insulation, replace an old inefficient appliance.

Worked example 5 A quick audit

A family lists: hot water ( $2500$ kWh/yr), fridge ( $400$ kWh/yr), TV ( $200$ kWh/yr), lighting ( $300$ kWh/yr), computer ( $150$ kWh/yr). Identify the biggest user and suggest one action.

Hot water is by far the biggest at $2500$ kWh/yr ( $\sim 70\%$ of this list).
Switching to a heat-pump or solar hot-water system could cut this by $60$ - $80\%$ , saving far more than LED bulbs would.

Key idea: tackle the biggest user first. Small gains on small users rarely beat a modest gain on the biggest one.

Practice: Year 8

Fluency

Watts, kW and kWh

Convert: (a) $800$ W to kW, (b) $2.4$ kW to W, (c) $1500$ W to kW.
A $100$ W bulb runs for $10$ hours. Energy used in kWh?
A $2$ kW heater runs for $3$ hours. Energy used in kWh?
A $50$ W fan runs for $8$ hours. Energy used in kWh?
At $0.30/kWh, find the cost of running a $1.5$ kW appliance for $2$ hours.

Fluency

Reading a bill

A meter starts at $10\,234$ kWh and reads $10\,859$ kWh at the end of the quarter. Find the usage.
A household used $720$ kWh at $0.28/kWh. What is the usage cost?
A daily supply charge is $1.10 for $91$ days. What is the total supply charge?
Add $10\%$ GST to a subtotal of $440.
Give three things an electricity bill typically shows.

Fluency

Efficiency labels

Appliance A uses $400$ kWh/yr, appliance B uses $500$ kWh/yr. At $0.30/kWh, what is the annual running cost of each?
A fridge has 4 stars and another has 2 stars. Which costs less to run?
Why are “kWh per year” labels more useful than just “watts”?
A 10-year old fridge uses $600$ kWh/yr, a new one $300$ kWh/yr. How much is saved over 5 years at $0.30/kWh?

Reasoning

Audit thinking

A family wants to reduce their bill. Should they replace their $60$ W LEDs or their $2000$ W electric heater? Explain.
Why might standby power (TV, microwave clocks) still matter?
Insulating a roof is expensive. How could you decide whether it is worth it?
Explain why hot-water heating is often the biggest single part of a household’s energy bill.

Problem solving

Applied contexts

A $200$ W computer is left on overnight ( $12$ hours) $200$ nights a year. At $0.30/kWh, find the annual cost.
A family runs a $3500$ W air conditioner $5$ hours a day for $60$ summer days. At $0.30/kWh, estimate the cost.
A household is considering a rooftop solar system that generates $5000$ kWh/yr. If their bill is $0.30/kWh, how much money would they avoid spending in the first year?
A home uses $1800$ kWh in winter and $900$ kWh in summer. Suggest why the winter figure is higher and predict two effective actions.

Challenge

Reasoning

Harder reasoning

A household has a $300$ L electric storage hot-water system rated at $3.6$ kW. It runs for about $3$ hours a day. Find the annual cost at $0.30/kWh, and suggest a lower-cost alternative with reasoning.
Two houses in the same street have identical appliances. House A pays $600 less per year for electricity. List three design or behaviour factors that could explain the difference.
A family installs LED lighting (saving $400$ kWh/yr) and a solar hot-water system (saving $1800$ kWh/yr) at a combined cost of $6000. Electricity is $0.30/kWh. Find the payback time in years.
Explain how a simple energy audit can lead to reductions in both household bills and Australia’s overall CO $_2$ emissions.

Answers

Answer key

Attempt the practice first. When you're ready to check, expand the answers below.

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Year 8 answers

Fluency

Watts, kW and kWh

(a) $0.8$ kW, (b) $2400$ W, (c) $1.5$ kW.
$0.1 \times 10 = 1$ kWh.
$2 \times 3 = 6$ kWh.
$0.05 \times 8 = 0.4$ kWh.
$1.5 \times 2 \times 0.30 = 0.90$ dollars.

Fluency

Reading a bill

$10\,859 - 10\,234 = 625$ kWh.
$720 \times 0.28 = 201.60$ dollars.
$91 \times 1.10 = 100.10$ dollars.
$440 \times 1.10 = 484.00$ dollars.
Any three of: meter readings (start and end), kWh used, tariff/price per kWh, supply charge, total cost, GST, billing period.

Fluency

Efficiency labels

A: $400 \times 0.30 = 120$ dollars/yr. B: $500 \times 0.30 = 150$ dollars/yr.
The 4-star fridge — more stars means more efficient, so less energy per year.
Watts only tell you power; “kWh per year” builds in how much and how often the appliance actually runs, which is what you actually pay for.
Difference $= 300$ kWh/yr. Annual saving $= 300 \times 0.30 = 90$ dollars. Over $5$ years, total saving $= 450$ dollars.

Reasoning

Audit thinking

Replace or reduce use of the heater. It draws $\sim 33\times$ more power than the LED and probably runs for hours each winter night, so it dominates the bill. LED lights are already low power.
Many appliances use several watts continuously, 24 hours a day. Across a whole home, standby can add up to 50-100 kWh/year — not huge individually, but meaningful and easy to cut.
Estimate the annual energy saved (lower heating/cooling kWh), multiply by the electricity tariff, then compare to the insulation cost. Payback time = cost / annual saving. If less than the life of the house, it is worthwhile.
Heating a large amount of water from cold to $\sim 60$ °C takes a lot of energy, and hot water is used every day year-round. Compared with a fridge (small steady draw) or lighting, hot water typically dominates.

Problem solving

Applied contexts

$0.2$ kW $\times 12$ h $= 2.4$ kWh/night. $\times 200 = 480$ kWh/yr. Cost $= 480 \times 0.30 = 144$ dollars/yr.
$3.5 \times 5 \times 60 = 1050$ kWh. Cost $= 1050 \times 0.30 = 315$ dollars.
$5000 \times 0.30 = 1500$ dollars avoided in year 1 (if all solar output replaces grid energy).
Winter is higher because of heating (and often hot water usage). Two effective actions: improve insulation/draughtproofing; replace old resistive heaters with a reverse-cycle heat pump, or add solar panels to offset grid use.

Reasoning

Challenge

Daily energy $= 3.6 \times 3 = 10.8$ kWh. Annual $= 10.8 \times 365 = 3942$ kWh. Cost $\approx 1183$ dollars/yr. Cheaper alternative: a heat-pump hot water system (roughly $3\times$ more efficient) or solar hot water — could cut the bill by $60$ - $80\%$ .
Any three of: better insulation; smaller or more efficient appliances; fewer people or hours at home; use of renewable energy (solar); lower thermostat settings; more natural light; turning off standby.
Total annual saving $= (400 + 1800) \times 0.30 = 660$ dollars/yr. Payback $= 6000 / 660 \approx 9.1$ years.
An audit targets the biggest energy users and waste. Replacing or switching them off cuts kWh, which lowers bills directly and, because grid electricity in Australia still includes a large share of fossil fuels, also cuts CO $_2$ emitted at power stations. If done across many homes, the total emission reduction is significant.

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