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.