Preview
IB DP Physics — Unit B: The Particulate Nature of Matter | SL & HL | B.2 Greenhouse Effect
📋 What You Will Learn
- Observe how the Sun's energy reaches Earth and understand why only a fraction is absorbed by the surface
- Define the solar constant, albedo, and emissivity, and explain the role each plays in Earth's energy balance
- Derive the effective temperature of Earth from first principles using the Stefan–Boltzmann law and the concept of radiative equilibrium
- Apply the energy balance equation to calculate effective surface temperatures for Earth and other planets
- Analyse how changes in albedo and emissivity alter the equilibrium temperature of a planet
- Evaluate the limitations of the simple energy balance model and connect this topic to the greenhouse effect and climate science
🌍 Real-World Context On a clear summer day, a dark asphalt road becomes scorching hot while a nearby snow-covered field stays cool — even though both receive the same sunlight. Fresh snow reflects roughly 80–90% of incoming solar radiation straight back into space, whereas dark asphalt absorbs nearly all of it. This single observation — that different surfaces interact with sunlight in fundamentally different ways — lies at the heart of how scientists calculate Earth's average temperature, model climate change, and even predict the surface conditions of distant planets. The question is: can we use these ideas to predict exactly how warm a planet should be, and why is Earth's actual temperature higher than this prediction?
🔍 Guiding Question How does the balance between incoming solar radiation and outgoing thermal radiation determine the equilibrium temperature of a planet, and what role do albedo and emissivity play in this balance?
Physical Setup: The Sun–Earth Energy System
The Sun continuously radiates energy in all directions as electromagnetic radiation, primarily in the visible and near-infrared parts of the spectrum. A tiny fraction of this energy reaches Earth, intercepted by the planet's cross-sectional area as though Earth were a flat disc facing the Sun. This intercepted energy is then either reflected back into space or absorbed by the surface and atmosphere, warming the planet.
A planet in a stable climate is neither continuously warming nor continuously cooling — it must be radiating energy back into space at the same average rate that it absorbs energy from the Sun. This condition is called radiative equilibrium , and it determines the planet's effective temperature. Understanding this balance requires us to carefully account for how much solar energy arrives, how much is reflected, and how efficiently the planet radiates energy away.
Notice the key geometric asymmetry in the diagram: Earth intercepts solar radiation over a circular cross-section of area \( \pi R_E^2 \), but it radiates thermal energy from its entire spherical surface of area \( 4\pi R_E^2 \). This factor of four is crucial — it appears directly in the derivation of Earth's effective temperature and is a common source of error in exam answers.
Core Concepts and Definitions
Before we can write any equations, we need to carefully define three quantities that govern the energy balance: the solar constant, albedo, and emissivity. Each one plays a distinct role — the solar constant tells us how much energy arrives, albedo tells us how much is reflected away, and emissivity tells us how efficiently the planet radiates energy back into space.
📖 Key Definition — Solar Constant (S) The solar constant \( S \) is the total power per unit area of solar electromagnetic radiation incident on a surface perpendicular to the Sun's rays, measured at the mean distance of Earth from the