Energy & efficiency

Conservation of energy

Energy can't be created or destroyed, only changed from one form to another. In real systems some energy is always "lost" as unwanted heat and sound, often through friction. An energy audit lists the energy in, the useful energy out and the losses.

Forms and sources of energy

Forms include kinetic, potential, heat (thermal), electrical, chemical, light, sound, nuclear and magnetic.

• Fossil fuels: coal, oil and gas: burned, so they release CO₂ and will run out.
• Nuclear: fission of uranium produces heat, which makes steam to turn a turbine and generator.
• Renewable: wind, wave, tidal, hydro-electric and solar.

Energy is the capacity to do work, measured in joules (J). Power is how fast energy is transferred, measured in watts (W = J/s). Think of energy as the fuel in the tank and power as how quickly it's used.

An energy transfer moves energy (electricity along wires); a transformation changes its form (chemical → kinetic). Every transformation wastes some energy, usually as heat and sound.

Prefixes and significant figures

Convert to base units before substituting, and convert time to seconds (7 minutes = 420 s). Give the final answer to 2 or 3 significant figures with its unit: 0.0078 A, 54%, 24 m/s.

Energy formulae

These are in the data booklet; you must be able to rearrange them and use the answer from one in the next.

Calculation technique

1. Write the formula.
2. Convert units first: hours to seconds (7.5 h = 27 000 s), kJ to J, mm to m where needed.
3. Substitute, then rearrange (transpose).
4. Give the answer to 2 significant figures with a unit.
5. Don't round in the middle of a calculation; round only the final answer.

Each step usually carries a mark: substitution, transposition and answer with unit. Follow-on marks mean a wrong earlier value doesn't stop you being awarded the later marks.

Worked examples: energy changing form

Potential to kinetic. A 50 kg object falls freely from 30 m. E_p = mgh = 50 × 9.8 × 30 = 14 700 J. All of it becomes kinetic energy at impact: 14 700 = ½ × 50 × v², so v² = 588 and v = 24 m/s.

Electrical to heat. A kettle uses 24 kJ to heat 2 kg of water to 100 °C (no losses). 24 000 = 4180 × 2 × ΔT, so ΔT = 2.87 °C and the water started at 97 °C.

Efficiency in three steps. A coffee machine (230 V, 22 A) heats 0.15 kg of water from 20 °C to 85 °C in 15 s.

1. Energy in: E_e = VIt = 230 × 22 × 15 = 75 900 J
2. Useful energy out: E_h = cmΔT = 4180 × 0.15 × 65 = 40 755 J
3. Efficiency: η = 40 755 ÷ 75 900 × 100 = 54%

The other 46% (35.1 kJ) is wasted, as heat to the casing and air, and sound. Efficiency can never be more than 100%.

Energy audits

An energy audit lists all the energy going into and coming out of a system, so you can see where energy is wasted. Total energy in = useful energy out + wasted energy. Show it as a diagram: the input on the left, the useful output on the right, and the waste (heat, sound) coming off the side, each labelled with its value.

Interactive simulation: try this on the revision site, where you can change the values and see the result.

Improving efficiency

Explain with a cause linked to the context and its effect: "Lubricate the gears (cause) to reduce friction, so less energy is lost as heat (effect)." Other examples: bearings, streamlining, insulation, reducing weight.

Design challenge: school lift energy audit

The brief. An Aberdeen school is replacing an old lift. The motor draws 15 A at 230 V for 20 s to lift 600 kg through 9 m.

1. Calculate the electrical energy supplied.
2. Calculate the potential energy gained.
3. Calculate the efficiency of the lift.
4. Explain two ways the new lift could be more efficient.

Higher energy problems HIGHER

Higher questions chain several formulae together. Example: a pump lifts 2500 litres (2500 kg) of water 2.9 m at 87% efficiency from a 230 V, 5 A supply. E_w = (2500 × 9.8) × 2.9 = 71 050 J; E_in = 71 050 ÷ 0.87 = 81 667 J; t = 81 667 ÷ (230 × 5) = 71 s.

Key terms

Quick check