The seven recognised forms of stored energy are listed below together with the usual formula and a short worked example. These formulas are useful for AO1 (knowledge) and AO2 (application) questions.
| Energy store | Typical formula | Example (simple calculation) |
|---|---|---|
| Kinetic energy | \(E_{k}= \dfrac12 mv^{2}\) | A 2 kg ball moving at 3 m s⁻¹ has \(E_{k}=0.5\times2\times3^{2}=9\ \text{J}\). |
| Gravitational potential energy | \(E_{g}= mgh\) | A 5 kg textbook lifted 0.8 m ( \(g=9.8\ \text{m s}^{-2}\) ) stores \(E_{g}=5\times9.8\times0.8\approx39\ \text{J}\). |
| Elastic (strain) energy | \(E_{e}= \dfrac12 kx^{2}\) ( \(k\)= spring constant, \(x\)= extension ) | A spring with \(k=200\ \text{N m}^{-1}\) compressed 0.05 m stores \(E_{e}=0.5\times200\times0.05^{2}=0.25\ \text{J}\). |
| Thermal (internal) energy | \(E_{th}= mc\Delta T\) ( \(c\)= specific heat capacity ) | Heating 0.5 kg of water (\(c=4180\ \text{J kg}^{-1}\text{K}^{-1}\)) from 20 °C to 30 °C: \(E_{th}=0.5\times4180\times10=20\,900\ \text{J}\). |
| Chemical energy | ΔH (enthalpy change of a reaction) or \(E_{ch}=Q\) released on combustion | Combusting 1 g of gasoline releases ≈ 44 kJ of chemical energy. |
| Electrostatic energy | \(E_{es}= \dfrac12 QV\) ( \(Q\)= charge, \(V\)= potential difference ) | A 10 µF capacitor charged to 100 V stores \(E_{es}=0.5\times10\times10^{-6}\times100^{2}=0.05\ \text{J}\). |
| Nuclear energy | \(E_{n}= \Delta mc^{2}\) (mass defect \(\Delta m\) ) | Fusion of four protons to one \(^4\!He\) nucleus releases ≈ 26.7 MeV ≈ \(4.3\times10^{-12}\ \text{J}\). |
Work is the transfer of energy when a force moves an object through a distance.
Example: Lifting a 5 kg textbook 0.8 m requires \(W = mgh = 5\times9.8\times0.8\approx39\ \text{J}\) (same as the gravitational‑PE example above).
Power is the rate at which work is done or energy is transferred.
Example: A 150 W solar panel delivers \(150\ \text{J}\) of energy each second.
For each of the main energy resources the syllabus expects you to state the primary form of energy, the usual conversion device, and one advantage and one disadvantage.
| Resource | Primary energy form | Typical conversion device | One advantage | One disadvantage |
|---|---|---|---|---|
| Chemical fuels (coal, oil, natural gas) | Chemical | Combustion turbine / internal‑combustion engine | Very high energy density | CO₂ emissions → climate change |
| Bio‑fuels | Chemical (derived from biomass) | Combustion engine or boiler | Renewable if sustainably sourced | Competes with food production for land |
| Hydroelectric | Gravitational potential | Water turbine | Very low operating emissions | Geographically limited; ecological impact on rivers |
| Geothermal | Thermal (heat from Earth’s interior) | Steam turbine | Reliable base‑load power | Location specific; high upfront cost |
| Nuclear fission | Nuclear | Pressurised water reactor (PWR) or boiling water reactor (BWR) | Large, steady power output | Radioactive waste and safety concerns |
| Solar photovoltaic (PV) | Solar radiation (photons) | Solar cells (silicon, perovskite, etc.) | Scalable, no moving parts | Intermittent; dependent on daylight |
| Solar thermal (concentrating) | Solar radiation (heat) | Concentrating mirrors + heat‑engine cycle | Can deliver high‑temperature heat for electricity | Requires large land area; intermittent |
| Wind | Kinetic (air movement) | Wind turbine | Low operating cost after installation | Variable output; visual/aesthetic impact |
| Tidal / wave | Mechanical (water movement) | Tidal barrage, oscillating water column, wave‑energy converter | Predictable, high‑density energy | Limited suitable sites; marine‑ecosystem impact |
Fusion is the process in which two light atomic nuclei combine to form a heavier nucleus. A small amount of the total mass is converted into a large amount of energy, as described by Einstein’s equation \(E = mc^{2}\).
\[\mathrm{^{1}H} + \mathrm{^{1}H} \;\rightarrow\; \mathrm{^{2}H} + e^{+} + \nu_{e}\]
(Energy released ≈ 0.42 MeV).
\[\mathrm{^{2}H} + \mathrm{^{1}H} \;\rightarrow\; \mathrm{^{3}He} + \gamma\]
(≈ 5.49 MeV).
\[\mathrm{^{3}He} + \mathrm{^{3}He} \;\rightarrow\; \mathrm{^{4}He} + 2\,\mathrm{^{1}H}\]
(≈ 12.86 MeV).
The mass of the four original protons is slightly greater than the mass of the resulting \(\mathrm{^{4}He}\) nucleus. The mass defect \(\Delta m\) is converted to energy:
\[E = \Delta m\,c^{2}\]
For the complete p‑p chain the total energy released is about 26.7 MeV per helium‑4 nucleus, i.e. \(4.3\times10^{-12}\ \text{J}\).
Question: After one complete p‑p chain, what is the net change in the number of free protons?
Answer: Two protons are consumed in step 1, one in step 2 and two are regenerated in step 3, so the net change is zero – the Sun acts as a catalyst for the cycle.
Fission splits a heavy nucleus into lighter fragments, releasing energy because the binding energy per nucleon decreases for very heavy elements.
Typical reaction (U‑235):
\[
\mathrm{^{235}U} + n \;\rightarrow\; \mathrm{^{141}Ba} + \mathrm{^{92}Kr} + 3n + \; \approx 200\ \text{MeV}
\]
Each fission event releases roughly 200 MeV, about eight times the energy from a single p‑p chain, but the fuel (uranium) is scarce and the process produces long‑lived radioactive waste.
For any energy‑conversion device the efficiency \(\eta\) is defined as
\[
\eta = \frac{\text{useful output energy (or power)}}{\text{total input energy (or power)}}\times100\%
\]
Example calculation – solar PV panel
This aligns with the typical 15–22 % efficiencies quoted for commercial silicon PV cells.
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