Solve problems involving energy and mass, including the joule and the watt, energy consumption measured in kilowatt-hours, the energy content of food measured in kilojoules, and daily energy requirements based on basal metabolic rate and level of activity

What this dot point is asking

NESA wants you to measure energy and use it in everyday decisions about electricity and food. Energy is measured in joules, and the rate at which energy is used is power, measured in watts. From there you need to do three practical jobs: work out how much electricity an appliance uses in kilowatt-hours and what it costs from a tariff; read the energy content of food in kilojoules and total it for a meal; and estimate a person's daily energy needs from their basal metabolic rate and how active they are. The arithmetic is gentle - mostly multiply and divide. The marks come from picking the right formula, keeping power in kilowatts and time in hours, and writing the unit on every answer.

The answer

There are two ideas to keep separate. Energy is the total amount of "work" done or heat produced, measured in joules ($\text{J}$). Power is how fast that energy is used, measured in watts ($\text{W}$), where $1$ watt is $1$ joule per second. An appliance's power rating (printed on it as a number of watts or kilowatts) tells you its power, and the longer it runs the more energy it uses. That single relationship runs the whole topic:

For electricity we measure energy in kilowatt-hours rather than joules, because joules are tiny for household amounts. Putting power in kilowatts and time in hours gives the energy straight in kilowatt-hours, and that is the "unit" you are billed for.

Joules and watts: energy and power

The base unit of energy is the joule ($\text{J}$). It is a small amount - lifting an apple about a metre is roughly one joule - so for everyday energy we use larger units like the kilojoule ($1$ kJ $= 1000$ J) for food, and the kilowatt-hour for electricity.

Power is the rate of using energy, measured in watts ($\text{W}$), where

So a $1000$ W appliance uses $1000$ joules every second. Because watts are small for whole appliances, ratings are often given in kilowatts ($1$ kW $= 1000$ W). A $2400$ W heater and a $2.4$ kW heater are the same thing. The key skill is moving between watts and kilowatts: divide by $1000$ going to kilowatts, multiply by $1000$ going back to watts.

Energy in kilowatt-hours

A kilowatt-hour ($\text{kWh}$) is the energy a $1$ kW appliance uses in $1$ hour. It is the "unit" of electricity on a bill. To find the energy an appliance uses, multiply its power in kilowatts by the time it runs in hours:

The two units must match the formula: power in kilowatts, time in hours. A $2$ kW heater for $3$ hours uses $2 \times 3 = 6$ kWh. A $150$ W ($0.15$ kW) fridge running all day uses $0.15 \times 24 = 3.6$ kWh. If a power is given in watts, convert to kilowatts first; if a time is given in minutes, convert to hours first (divide by $60$).

The cost of running an appliance

Electricity is priced as a tariff: so many cents or dollars per kilowatt-hour. Once you have the energy in kilowatt-hours, the cost is just the energy times the price per unit:

A $2.4$ kW air conditioner running $5$ hours uses $2.4 \times 5 = 12$ kWh, and at $0.30 per kWh that costs $12 \times 0.30 = 3.60$, that is $3.60. Keep the tariff in dollars (a $30$ c tariff is $0.30) so the answer comes out in dollars. Many bills also have a fixed daily supply charge added on top; unless a question gives one, the usage cost is the energy times the tariff.

Food energy in kilojoules

The energy in food is measured in kilojoules ($\text{kJ}$); it is the chemical energy your body can release from the food. (You may see the old unit, the Calorie, where $1$ Cal $\approx 4.2$ kJ, but Australian labels and NESA use kilojoules.) Food energy is additive: the energy of a meal is the sum of the energy of its parts. Labels often quote energy "per $100$ g", so for a different amount you scale:

For example, butter at $3000$ kJ per $100$ g gives $\tfrac{10}{100} \times 3000 = 300$ kJ in a $10$ g serve.

Daily energy needs: BMR times activity

Your body uses energy even at complete rest - to breathe, pump blood and stay warm. That baseline rate is the basal metabolic rate (BMR), in kilojoules per day. Being active uses more, so your total daily need is the BMR scaled up by a physical activity level (PAL), also called an activity factor:

A sedentary person has a PAL near $1.4$; someone moderately active is around $1.6$ to $1.75$; a very active person can be over $2$. So a BMR of $7000$ kJ with a PAL of $1.6$ gives $7000 \times 1.6 = 11\,200$ kJ per day. The average-adult reference figure you see on packaging is $8700$ kJ, which is a population average, not a personal target. Comparing a meal or a day's needs to $8700$ kJ as a percentage is a common exam step: divide by $8700$ and multiply by $100$.

Weight stays steady when the energy you eat balances the energy you use. The schematic compares the energy coming in as food with the energy going out as your basal metabolic rate plus activity. When the two columns match, energy is balanced; if the food column is taller the surplus is stored, and if it is shorter the body draws on its stores.

How exam questions ask about energy and nutrition

The wording tells you which formula to reach for:

• "What is the power rating ... in kilowatts / in watts" is a watt-kilowatt conversion: divide by $1000$ to kilowatts, multiply by $1000$ to watts.
• "How much energy ... in kWh" or "how many units of electricity" wants $\text{power (kW)} \times \text{time (h)}$ - convert watts to kilowatts and minutes to hours first.
• "How much does it cost to run ..." wants the energy in kWh times the tariff; write the tariff in dollars and watch for a per-day, per-week or per-year time span.
• "How much would they save ..." asks for the difference between two costs (a higher and a lower tariff, or longer and shorter run time).
• "Find the total energy of the meal / how many kilojoules" wants you to add the kilojoule figures, scaling any per-$100$-g item first.
• "Estimate the daily energy requirement" wants $\text{BMR} \times \text{PAL}$; if a PAL is described in words ("moderately active"), use the value the question supplies.
• "As a percentage of the recommended intake" means divide by the reference (usually $8700$ kJ) and multiply by $100$.