Know that energy is released by nuclear fusion in the Sun

1.7 Energy, Work and Power – Energy Resources

1.7.1 Energy Stores (core requirement)

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 ≈ \(4.3\times10^{-12}\ \text{J}\).

1.7.2 Work (core requirement)

Work is the transfer of energy when a force moves an object through a distance.

• Mechanical work: \(W = Fd\) (\(F\) in newtons, \(d\) in metres).
• Electrical work: \(W = VIt\) (\(V\) voltage, \(I\) current, \(t\) time).

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).

1.7.3 Power (core requirement)

Power is the rate at which work is done or energy is transferred.

• \(P = \dfrac{W}{t}\) or \(P = \dfrac{\Delta E}{t}\) (\(\text{W} = \text{J s}^{-1}\)).

Example: A 150 W solar panel delivers \(150\ \text{J}\) of energy each second.

1.7.4 Energy Resources – Core

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

Solar Energy – Nuclear Fusion in the Sun

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 \(E = mc^{2}\).

Why the Sun is a natural fusion reactor

• Core temperature ≈ \(1.5\times10^{7}\ \text{K}\).
• Core pressure ≈ \(2.5\times10^{11}\ \text{Pa}\).
• These extreme conditions give protons enough kinetic energy to overcome their electrostatic (Coulomb) repulsion and fuse.

Proton–Proton (p‑p) chain – dominant solar fusion process

1. Two protons fuse to form deuterium, a positron and a neutrino \[\mathrm{^{1}H} + \mathrm{^{1}H} \;\rightarrow\; \mathrm{^{2}H} + e^{+} + u_{e}\] (Energy released ≈ 0.42 MeV).
2. Deuterium captures a third proton, producing helium‑3 and a gamma photon \[\mathrm{^{2}H} + \mathrm{^{1}H} \;\rightarrow\; \mathrm{^{3}He} + \gamma\] (≈ 5.49 MeV).
3. Two helium‑3 nuclei combine to give helium‑4 and two protons (which re‑enter the cycle) \[\mathrm{^{3}He} + \mathrm{^{3}He} \;\rightarrow\; \mathrm{^{4}He} + 2\,\mathrm{^{1}H}\] (≈ 12.86 MeV).

Energy released

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. \(4.3\times10^{-12}\ \text{J}\).

Quick‑check (AO2)

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.

Comparison with nuclear fission (supplementary)

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.

1.7.5 Efficiency of Energy Conversion (supplementary requirement)

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

• Solar irradiance \(I = 1000\ \text{W m}^{-2}\) (typical clear‑sky value).
• Panel area \(A = 0.20\ \text{m}^{2}\) → incident power \(P_{in}= I A = 200\ \text{W}\).
• Panel rating \(P_{out}= 30\ \text{W}\) (as measured).
• \(\displaystyle \eta = \frac{30}{200}\times100\% = 15\%\).

This aligns with the typical 15–22 % efficiencies quoted for commercial silicon PV cells.

1.7.6 Practical / Experimental Connections (AO2)

• Measuring solar power: Use a calibrated solar‑panel meter to record power output (W) at different times of day. Compare the measured values with the theoretical power \(P = I A\) where \(I\) is the measured solar irradiance.
• Energy‑mass conversion demonstration: Weigh a sealed radioactive source before and after a short decay period with a high‑precision balance. The change in mass is far below the instrument’s resolution, reinforcing that the mass loss in fusion/fission is extremely small but corresponds to a large energy release via \(E=mc^{2}\).
• Safety note: When handling any radioactive material or high‑current equipment, wear appropriate PPE, work in a well‑ventilated area, and follow school laboratory safety procedures.

1.7.7 Key Points to Remember (AO1)

• The seven energy stores are kinetic, gravitational PE, elastic, thermal, chemical, electrostatic and nuclear.
• Work = force × distance (mechanical) or voltage × current × time (electrical). Power = work ÷ time.
• Solar energy originates from nuclear fusion in the Sun’s core via the proton–proton chain, releasing ≈ 26.7 MeV per \(\mathrm{^{4}He}\) nucleus.
• Mass loss in fusion is converted to energy by \(E = mc^{2}\); the Sun’s total power output is about \(3.8\times10^{26}\ \text{W}\).
• Each energy resource can be described by its primary energy form, a typical conversion device, one advantage and one disadvantage (see the core table).
• Efficiency \(\eta\) measures how much useful energy is obtained from a given input; solar PV panels typically operate at 15–22 % efficiency.
• Fission and fusion both release nuclear energy, but fission splits heavy nuclei (e.g., \(\mathrm{^{235}U}\)) while fusion joins light nuclei (e.g., the p‑p chain). Fusion produces less radioactive waste but requires far higher temperature and pressure.
• Understanding solar fusion underpins the development of renewable technologies such as photovoltaic cells and concentrating solar‑thermal power.