The big idea: Stand right by a campfire and its warmth is fierce; step back and the same fire barely reaches you — how much radiation power lands on each square metre is its intensity.
The Sun pours out power in all directions, and the further away you are the more thinly it spreads, so the intensity you receive is smaller.
Unit: W m⁻² (watts per square metre).
Intensity triangle: P = power (W), I = intensity (W m⁻²), A = area (m²). Cover the one you want — two side by side → multiply; one above the other → divide.
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Spreading thins it out: The Sun's power spreads over the surface of an ever-growing sphere as it travels outward.
Same total power, bigger area → smaller intensity. That is why it is hotter on Mercury than on Earth.
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Intensity = the radiation power divided by the area it is spread over. It is a simple quotient, so use a formula triangle.
- intensity (W m⁻²)
- radiation power passing through the area (W)
- area the power spreads over (m²)
Spreading over a sphere: A source sending power out equally in all directions spreads it over the surface of a sphere.
A sphere of radius d has area A = 4πd², so the intensity a distance d away is:
- intensity at the distance d (W m⁻²)
- total power radiated by the source (W)
- distance from the source (m)
The solar constant: The solar constant is the intensity of the Sun's radiation arriving at Earth's distance, measured just above the atmosphere.
Its value is S = 1.36 × 10³ W m⁻² — given in the data booklet.
A small lamp radiates 60 W of light equally in all directions. Find the intensity 2.0 m away.
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How this is tested — the solar constant and intensity turn up in the climate / energy-balance questions:
Paper 1A
- A solar panel's power output from intensity × area × efficiency.
- Or how intensity changes when you double the distance.
Paper 2
- A 'state' mark for what the solar constant means.
- Then a 'show that' — work the Sun's total power back with P = I × 4πd².
The classic trap: Inverse-square: double the distance → intensity drops to a quarter, not a half (the d is squared).
Power, intensity and a sphere: To get the total power a source radiates, multiply the intensity at distance d by the whole sphere area 4πd²:
P = I × 4πd².
For solar panels, the useful output is the incident power on the panel × its efficiency.
The solar constant is S = 1.36 × 10³ W m⁻². The Earth orbits the Sun at a distance d = 1.5 × 10¹¹ m. Show that the total power radiated by the Sun is about 4 × 10²⁶ W.
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