Where the Sun's energy comes from
The Sun is a huge ball of hot gas, mostly hydrogen. In its core the temperature is about 15 million K. There, hydrogen nuclei crash together so hard that they fuse into helium. This is nuclear fusion.
The helium made has slightly less mass than the hydrogen that went in. The missing mass becomes energy: E = mc² (c = 3 × 10⁸ m/s). Because c² is so big, a tiny mass gives a huge energy. The Sun turns about 4 million tonnes of mass into energy every second.
This energy slowly travels out and leaves the surface as electromagnetic radiation: visible light, infrared (heat) and some ultraviolet. Almost all our energy, including food, wind, rain and fossil fuels, began as sunlight.
The Sun's radiation: Wien's law and Stefan's law
Every hot object glows. Its colour and brightness depend on its temperature.
Wien's law: colour tells temperature
The wavelength where an object glows brightest gets shorter as it gets hotter: λmax × T = 2.9 × 10⁻³ m·K. The Sun's surface (T ≈ 5800 K) peaks at about 500 nm, in the visible light. A heater at 900 K peaks in the infrared, so it glows dull red. A blue star is hotter than a red one.
Stefan's law: hotter means much brighter
The power given off by each square metre of surface is P/A = σT⁴, with σ = 5.67 × 10⁻⁸ W m⁻² K⁻⁴. Doubling the temperature makes it 2⁴ = 16 times stronger.
How much power reaches Earth? Latitude and seasons
The Sun's power spreads out over a bigger and bigger sphere. At Earth's distance (150 million km), a 1 m² surface facing the Sun just outside the atmosphere gets about 1361 W. This is the solar constant.
- The atmosphere reflects and absorbs some, so on a clear day at noon about 1000 W/m² reaches the ground.
- Averaged over the whole spinning globe, day and night, Earth gets about 340 W/m² at the top of the atmosphere (1361 ÷ 4, because a sphere has 4 times the area of its shadow disc).
- About 30% is reflected straight back (the albedo); the rest warms land, sea and air.
Why the poles are cold
Near the equator the Sun is high and rays hit the ground nearly straight on. Near the poles the same beam hits at a slant and spreads over a larger area, so each square metre gets less: intensity on the ground ≈ intensity × sin(Sun's height). The slanted rays also pass through more air.
Seasons
Earth's axis is tilted by about 23.5°. In June the northern half leans toward the Sun: the Sun is higher and days are longer, so it is summer there and winter in the south. Six months later it is the opposite. Seasons are caused by the tilt, not by Earth being closer to the Sun.
Solar cells (photovoltaics) and solar heating
A solar cell is a thin slice of silicon made of two layers (a p–n junction). Light gives electrons enough energy to break free, and the junction pushes them one way, so a current flows. Many cells joined make a panel.
Power: P = light intensity (W/m²) × area (m²) × efficiency (η) × cos(tilt angle away from the Sun). Common panels have η ≈ 15–22%.
The I–V curve
Connect a cell to a variable resistor, an ammeter and a voltmeter, and measure current I and voltage V for many loads. The graph is flat at first (current nearly fixed: the short-circuit current), then drops steeply near the open-circuit voltage (about 0.6 V for one silicon cell). Power P = V × I is greatest at the "knee" of the curve: the maximum power point (MPP).
More light raises the current almost in proportion, so the power goes up roughly in step with light intensity; the voltage changes only a little. Heat lowers the voltage, so hot panels work slightly worse.
From panel to home
Panels give direct current (DC). An inverter changes it to alternating current (AC) for the home or the grid. Modern inverters use MPP tracking: they keep adjusting the load so the panel always works at its maximum power point. Batteries store energy for the night.
Solar thermal
A solar water heater uses black pipes or plates (black absorbs best) under glass (which traps heat) to warm water. Solar cookers and concentrated solar power plants use mirrors to focus sunlight.
Good and not so good
Solar energy is renewable, free once installed, and makes no smoke. But it does not work at night, gives less on cloudy days, and needs a lot of space and storage.
Try it: measure sunlight with your hands
Hold a torch straight down over a sheet of squared paper and count the squares it lights. Now tilt the torch: the same light spreads over more squares, so each square gets less. This is why winter sunshine is weaker and why panels are tilted to face the Sun. If you have a small solar toy or calculator, cover half its cell and watch it slow down.
Key formulas and definitions
- E = mc²
- Wien: λmax × T = 2.9 × 10⁻³ m·K
- Stefan: P/A = σT⁴, σ = 5.67 × 10⁻⁸ W m⁻² K⁻⁴
- Solar constant ≈ 1361 W/m²; at ground ≈ 1000 W/m²
- Panel power P = I × A × η × cos θ
- Electrical power P = V × I
Worked examples
1. A 1.5 m² panel with 20% efficiency faces the Sun in 1000 W/m² sunlight. Find its power.
P = 1000 × 1.5 × 0.20 = 300 W.
2. The same panel is tilted 60° away from the Sun. What is its power now?
cos 60° = 0.5, so P = 300 × 0.5 = 150 W.
3. A home uses 6 kWh a day. Panels give an average of 1.2 kW for 5 sunny hours. Is that enough?
Energy = 1.2 kW × 5 h = 6 kWh. Yes, just enough on a sunny day.
4. Using Wien's law, find the peak wavelength of the Sun (T = 5800 K).
λ = 2.9 × 10⁻³ ÷ 5800 = 5 × 10⁻⁷ m = 500 nm (green-blue visible light).
5. A star has twice the surface temperature of the Sun. How much more power does each m² give out?
P/A ∝ T⁴, so 2⁴ = 16 times more.
6. From an I–V test a cell gives (0.40 V, 2.8 A), (0.48 V, 2.5 A) and (0.55 V, 1.5 A). Which point is closest to the MPP?
P = 1.12 W, 1.20 W and 0.83 W. The middle point (0.48 V, 2.5 A) gives the most power.
Common mistakes
- Saying the Sun "burns" like a fire. It does not burn fuel with oxygen; it fuses nuclei.
- Thinking seasons happen because Earth is closer to the Sun in summer. They are caused by the 23.5° tilt.
- Forgetting efficiency: a 2 m² panel in 1000 W/m² does not give 2000 W; at 20% it gives 400 W.
- Using the solar constant (1361 W/m²) for a panel on the ground; use about 1000 W/m² or less.