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5C

Energy and fuel consumption rates

Converting between L/100 km and km/L, comparing petrol, hybrid and electric cars by cost per kilometre and per year, payback time for a more efficient car, gas use in MJ, and solar power savings.

Fuel and energy are paid for by the litre, the kilowatt-hour or the megajoule, but used per kilometre or per hour. Comparing two cars, two heaters or two power plans means turning everything into the same rate first. This section is about making those comparisons fairly.

Revise: trip costs from L/100 km and EV charging are in Year 11 Running a car, and kWh = kW × h is in Year 11 Energy at home and in food.

L/100 km and km/L

Australia labels cars in litres per $100$ km: smaller is better, because the car uses less fuel. Some countries, and many drivers, think in kilometres per litre: there, bigger is better. The two are reciprocals, so you can always flip one into the other through $100$.

Converting fuel consumption

$\text{km/L} = \dfrac{100}{\text{L/100 km}}$ and $\text{L/100 km} = \dfrac{100}{\text{km/L}}$

Example 1●

A ute travels $14$ km on each litre. Write this in L/100 km. Then convert $8$ L/100 km to km/L.

$100 \div 14 \approx 7.14$ L/100 km
To go 100 km at 14 km per litre you need 100 ÷ 14 litres.
$100 \div 8 = 12.5$ km/L
8 litres take you 100 km, so 1 litre takes you 100 ÷ 8 km.

Comparing vehicles

To compare a petrol car with an electric one, put both into the same money rate, such as dollars per $100$ km. Then scale to the distance you actually drive.

Example 2●●

A small petrol car uses $6.5$ L/100 km with petrol at $195$c/L. An electric car uses $16$ kWh/100 km, charged at home at $30$c/kWh. Compare their running costs per $100$ km.

Petrol: $6.5 \times \$1.95 \approx \$12.68$ per $100$ km
Cost per 100 km = amount per 100 km × price per unit.
Electric: $16 \times \$0.30 = \$4.80$ per $100$ km
Same idea for electricity, priced per kWh.
The electric car costs about $\$7.88$ less per $100$ km to run at these prices.
Compare like with like.
InteractiveTrip cost planner
Try this

Set a $450$ km trip and check Example 2 against the cost per $100$ km for the small car and the electric car. Then raise petrol to $230$c/L: how much more does the SUV trip cost? Finally find the electricity price at which the electric car costs the same per km as the hybrid.

Example 3●●●

A family drives $15{,}000$ km a year. An SUV uses $9.8$ L/100 km and a hybrid $4.2$ L/100 km, with petrol at $\$1.95$/L. The hybrid costs $\$6000$ more to buy. How long until the fuel savings pay back the extra price?

SUV: $9.8 \times 150 = 1470$ L. Hybrid: $4.2 \times 150 = 630$ L.
Fuel per year = L/100 km × (km ÷ 100).
SUV: $1470 \times 1.95 = \$2866.50$. Hybrid: $630 \times 1.95 = \$1228.50$.
Multiply by the price.
$2866.50 - 1228.50 = \$1638$ per year
Saving per year is the difference.
$6000 \div 1638 \approx 3.7$ years
Payback time = extra cost ÷ saving per year. This is a break-even point, just like in Chapter 1.

Gas and solar

Gas is billed in megajoules (MJ). Gas heaters and cooktops are rated in MJ per hour, so the energy used is the rate times the time. Recall $1$ kWh $= 3.6$ MJ.

Example 4●●

A gas heater is rated at $25$ MJ/h and runs for $4$ hours. Gas costs $4.2$c/MJ. Find the cost, and the energy in kWh.

$25 \times 4 = 100$ MJ
Energy = rate × time.
$100 \times \$0.042 = \$4.20$
Cost = energy × price per MJ.
$100 \div 3.6 \approx 27.8$ kWh
Divide by 3.6 to change MJ to kWh.
Example 5●●

On a sunny day, a home's solar panels generate $22$ kWh. The home uses $9$ kWh of it, which saves buying power at $33$c/kWh, and exports the other $13$ kWh for a feed-in tariff of $5$c/kWh. What is the day's benefit?

$9 \times \$0.33 = \$2.97$
Power used at home saves the full retail price.
$13 \times \$0.05 = \$0.65$
Exported power earns only the feed-in tariff.
$\$2.97 + \$0.65 = \$3.62$ for the day
Add the two.

Your turn

A car is advertised at $5.6$ L/100 km. How many km/L is that, and how much fuel would a $380$ km trip use?

Show the working

$100 \div 5.6 \approx 17.9$ km/L. Fuel: $5.6 \times 380 \div 100 = 21.28$ L.

Flashcards
L/100 km ↔ km/L
Divide 100 by the other number
Payback time
Extra purchase cost ÷ saving per year
1 kWh in MJ
3.6 MJ
Practice

  1. Convert $8$ L/100 km to km/L.

  2. Convert $14$ km/L to L/100 km, to $2$ decimal places.

  3. Which car is the most fuel efficient?

  4. An electric car uses $16$ kWh/100 km and power costs $30$c/kWh. What is the cost, in dollars, per $100$ km?

  5. A car uses $9.8$ L/100 km. How many litres does it use in $15{,}000$ km?

  6. At $\$1.95$/L over $15{,}000$ km, how much does a $4.2$ L/100 km hybrid save, in dollars, compared with a $9.8$ L/100 km SUV?

  7. A heater rated at $25$ MJ/h runs for $4$ hours with gas at $4.2$c/MJ. What is the cost, in dollars?

  8. Solar power used at home is worth more than solar power exported because:

  9. Exam style: Panels make $22$ kWh in a day. $9$ kWh is used at home (saving $33$c/kWh) and the rest is exported at $5$c/kWh. What is the total benefit, in dollars?

  10. Exam style: A hybrid costs $\$6000$ more than an SUV and saves $\$1638$ a year in fuel. How many years does it take to pay back the extra cost, to $1$ decimal place?

Formula sheet