B.2 Greenhouse effectIB Physics HL: Revision notes

The Earth's temperature is set by the conservation of energy: in equilibrium, the power absorbed from the Sun equals the power radiated back to space.

The solar constant S is the intensity of the Sun's radiation at the Earth's mean distance, on a surface perpendicular to the rays (about 1361 W m⁻²). The Earth intercepts sunlight over its projected area, a disc of area πR², but radiates from its whole surface, 4πR². So the mean incoming intensity over the whole surface is

$\frac{\pi R^2 S}{4\pi R^2} = \frac{S}{4}$

Albedo is the fraction of incident radiation that is scattered or reflected:

$\text{albedo} = \frac{\text{total scattered power}}{\text{total incident power}}$

The Earth's mean albedo is about 0.3. It varies daily with cloud formations (clouds are very reflective) and with latitude (snow and ice near the poles are highly reflective; oceans and forests absorb well).

Emissivity e compares a surface's emission with that of a black body at the same temperature:

$e = \frac{\text{power radiated per unit area}}{\sigma T^4}$

so a real surface radiates $e\sigma AT^4$. A black body has e = 1.

In equilibrium: $(1 - \alpha)\frac{S}{4} = e\sigma T^4$.

The main greenhouse gases are methane CH₄, water vapour H₂O, carbon dioxide CO₂ and nitrous oxide N₂O. Each has natural and human (anthropogenic) sources:

• CO₂: respiration, volcanoes / burning fossil fuels, deforestation
• CH₄: wetlands / livestock, rice paddies, landfill, gas leaks
• H₂O: evaporation from oceans / (human effect mainly indirect, via warming)
• N₂O: soil bacteria / nitrogen fertilisers, industry

The Sun is hot, so its radiation peaks in the visible; this passes through the atmosphere largely unabsorbed. The Earth's surface is much cooler (≈ 288 K) and emits infrared, peaking around 10 μm.

Molecular energy level model: greenhouse-gas molecules have vibrational energy levels whose separations match the energies of infrared photons. A molecule absorbs a photon and moves to a higher vibrational level, then de-excites, emitting infrared in all directions — some back towards the surface.

Resonance model: the bonds in these molecules have natural frequencies of vibration in the infrared range. Infrared radiation at these frequencies drives the molecules into resonance, so energy is absorbed strongly.

The returned radiation means the surface must reach a higher temperature to lose energy at the same rate as it gains it: this is the greenhouse effect. Without it, the Earth's mean temperature would be about 255 K rather than 288 K.

The enhanced greenhouse effect is the increase in the greenhouse effect caused by human activities that raise greenhouse-gas concentrations — CO₂ has risen from about 280 ppm before industrialisation to over 420 ppm. More infrared is absorbed and returned, so the effective emissivity of the Earth–atmosphere system falls and the equilibrium surface temperature rises.

Feedbacks can amplify the change: melting ice reduces albedo, and a warmer atmosphere holds more water vapour, itself a greenhouse gas.