# Greenhouse effect

> IB Physics HL · IB Physics Higher Level (2025+ syllabus)
> Source: https://www.owlsprep.com/study/ib-physics-hl-u2-greenhouse-effect/

This module covers the physical basis of the natural greenhouse effect, key gas properties, Earth's energy balance, albedo effects, and anthropogenic enhanced warming for IB HL assessment.

**Prerequisites:** [Black body radiation and Stefan-Boltzmann law](https://www.owlsprep.com/study/ib-physics-hl-u2-black-body-radiation/); [Electromagnetic spectrum and photon energy](https://www.owlsprep.com/study/ib-physics-hl-u2-electromagnetic-spectrum/)

## Learning objectives

- Explain the physical mechanism of greenhouse gas absorption of terrestrial infrared radiation
- Derive and apply the simple Earth energy balance model to calculate equilibrium surface temperature
- Distinguish between the natural life-sustaining greenhouse effect and anthropogenic enhanced greenhouse effect
- Analyze how albedo changes modify global average atmospheric temperatures

## Core Physical Mechanism of the Greenhouse Effect

Short-wavelength solar radiation (peak ~500 nm, visible spectrum) passes unabsorbed through the lower atmosphere to heat the Earth's surface. The warm surface then emits longer-wavelength infrared (IR) radiation, which interacts with greenhouse gas molecules in the atmosphere.

**IR-active greenhouse gas** — A gas molecule with an asymmetric dipole moment that can be excited to a higher vibrational energy level by absorbing an IR photon of matching energy.

*Example:* CO₂, H₂O, CH₄, N₂O are all IR-active; symmetric diatomics N₂ and O₂ are not.

> **info**
>
> Excited greenhouse gas molecules re-emit the absorbed IR photon in a random direction, including back towards the Earth's surface, adding extra thermal energy to the lower atmosphere.

**Worked example:** Calculate the approximate peak wavelength of radiation emitted by the Earth's 290 K surface, using Wien's displacement law \(\lambda_{max} T = 2.9 \times 10^{-3} \text{ m K}\)

1. Rearrange Wien's law to solve for peak wavelength
2. $$\(\lambda_{max} = \frac{2.9 \times 10^{-3}}{290}\)$$
3. Calculate the result
4. $$\(\lambda_{max} = 1.0 \times 10^{-5} \text{ m} = 10 \, \mu \text{m}\)$$
5. This falls in the long-wavelength IR range that is strongly absorbed by CO₂ molecules.

**Check your understanding**

Confirm your understanding of molecular absorption:

1. Which of these gases is a primary greenhouse gas?

   - N₂
   - O₂
   - CO₂
   - Ar

   *Why:* CO₂ has an asymmetric vibrational mode that absorbs IR radiation, unlike the symmetric diatomics N₂ and O₂.

## Earth Energy Balance and Equilibrium Temperature

**Derivation:** Derive the Earth's no-atmosphere equilibrium temperature

*Starting from:* Incoming total solar power absorbed by Earth equals total power radiated out to space at steady state

1. Average incident solar power per unit area across the full spherical Earth surface is the solar constant divided by 4
2. $$\(P_{in} = \frac{S}{4}(1-\alpha)\)$$
3. Total power radiated per unit area from the Earth's surface follows the Stefan-Boltzmann law
4. $$\(P_{out} = \sigma T^4\)$$
5. Set incoming and outgoing power equal for equilibrium
6. $$\(\frac{S}{4}(1-\alpha) = \sigma T^4\)$$
7. Rearrange to solve for temperature T
8. $$\(T = \sqrt[4]{\frac{S(1-\alpha)}{4\sigma}}\)$$

*Conclusion:* For S=1360 W/m², α=0.3, this gives T=255 K (-18°C) for a no-atmosphere Earth.

> **Exam tip**
>
> You will be asked to show this derivation in 3-4 mark Paper 2 questions, so ensure you explicitly state the S/4 factor comes from the spherical geometry of the Earth.

**Worked example:** Calculate the new equilibrium temperature if the global average albedo drops from 0.3 to 0.25 due to Arctic sea ice melt.

1. Substitute all known values into the equilibrium temperature formula
2. $$\(T = \sqrt[4]{\frac{1360 \times (1-0.25)}{4 \times 5.67 \times 10^{-8}}}\)$$
3. Simplify the numerator and denominator terms
4. $$\(T = \sqrt[4]{\frac{1020}{2.268 \times 10^{-7}}} = \sqrt[4]{4.497 \times 10^9}\)$$
5. Calculate the final temperature
6. $$\(T = 259 \, \text{K} = -14 ^\circ \text{C}\)$$
7. This 4 K temperature rise demonstrates the positive ice-albedo feedback effect.

*Calculator:* allowed

## Albedo Variations and Feedback Loops

| Surface type | Typical albedo value |
| --- | --- |
| Fresh snow | 0.8 - 0.9 |
| Open ocean water | 0.06 |
| Tropical forest | 0.15 |
| Desert sand | 0.4 |
| Cumulus cloud | 0.7 |

Positive feedback loops occur when an initial temperature change drives a secondary effect that amplifies the original change. The most commonly examined example is Arctic ice melt: rising temperatures reduce sea ice coverage, exposing low-albedo ocean water that absorbs more solar radiation, causing further warming and more ice melt.

**Worked example:** Calculate the percentage change in absorbed solar power per unit area if 1 m² of albedo 0.8 sea ice is replaced by albedo 0.1 open ocean.

1. Calculate absorbed power for sea ice
2. $$\(P_{ice} = \frac{S}{4}(1-0.8) = 340 \times 0.2 = 68 \text{ W m}^{-2}\)$$
3. Calculate absorbed power for open ocean
4. $$\(P_{ocean} = 340 \times (1-0.1) = 306 \text{ W m}^{-2}\)$$
5. Find the percentage increase
6. $$\(\Delta P \% = \frac{306 - 68}{68} \times 100 = 350 \%\)$$

## Enhanced Greenhouse Effect and Impacts

**Exam command terms**

IB exam questions use specific command terms for this topic:

- **Distinguish** — State clear differences between natural and enhanced greenhouse effect *(You must explicitly note the natural effect is essential for life, while the enhanced effect is anthropogenic.)*

- **Evaluate** — Justify a conclusion using quantitative temperature data *(Compare the 33°C natural greenhouse warming to the 1.1°C observed anthropogenic warming since 1900.)*

> **warning**
>
> Never claim the greenhouse effect is 'bad' or entirely human-caused in exams: you will lose marks for failing to acknowledge the natural 33°C warming that makes liquid water on Earth possible.

**Worked example:** Identify two anthropogenic activities that directly increase atmospheric CO₂ concentrations and drive the enhanced greenhouse effect.

1. 1. Combustion of fossil fuels for electricity generation, transport and industry releases geologically sequestered carbon as CO₂ into the atmosphere.
2. 2. Deforestation removes forest carbon sinks, reducing the rate at which atmospheric CO₂ is absorbed via photosynthesis.

## Common pitfalls

- **Wrong:** Stating greenhouse gases absorb incoming short-wavelength visible solar radiation
  - Why it fails: Visible solar radiation passes almost unimpeded through the atmosphere; only outgoing long-wavelength terrestrial IR is absorbed
  - Correct: Explicitly note the absorption targets radiation emitted by the Earth's surface, not incoming solar radiation
- **Wrong:** Forgetting to divide the solar constant by 4 in equilibrium temperature calculations
  - Why it fails: The solar constant is defined for a flat surface perpendicular to sunlight, but the spherical Earth distributes this power across 4x its cross-sectional area
  - Correct: Always use average incident power per unit area of S/4 = ~340 W/m² for global energy balance
- **Wrong:** Listing N₂ and O₂ as primary greenhouse gases
  - Why it fails: Symmetric diatomic molecules have no net dipole moment, so their vibrational modes cannot absorb IR photons
  - Correct: Only name IR-active asymmetric molecules: CO₂, H₂O, CH₄, N₂O as primary greenhouse gases
- **Wrong:** Confusing albedo and emissivity in the energy balance equation
  - Why it fails: Albedo describes reflected incoming radiation, emissivity describes the fraction of black body radiation emitted to space
  - Correct: Keep separate terms for reflected fraction (α) and emitted fraction (e) in all calculations
- **Wrong:** Claiming the greenhouse effect is entirely anthropogenic
  - Why it fails: The natural greenhouse effect warms the Earth by 33°C from -18°C to 15°C, which is essential for all known life
  - Correct: Clearly distinguish the natural life-sustaining effect from the anthropogenic enhanced effect driven by excess emissions

## Cheatsheet

| Quantity | Definition | Standard Value | Exam Formula |
| --- | --- | --- | --- |
| Solar constant S | Incident solar power at top of atmosphere | 1360 W m⁻² | \(P_{in} = \frac{S}{4}(1-\alpha)\) |
| Albedo α | Fraction of incoming radiation reflected | 0.3 (global average) | \(\alpha = P_{reflected} / P_{incident}\) |
| Stefan-Boltzmann constant σ | Black body radiation proportionality | 5.67 × 10⁻⁸ W m⁻² K⁻⁴ | \(P_{out} = \sigma T^4\) |
| Equilibrium temperature | Steady state surface temperature | 288 K (15°C) | \(T = \sqrt[4]{\frac{S(1-\alpha)}{4\sigma}}\) |

## What's next

Now that you have mastered the greenhouse effect and energy balance model, you can apply these core thermal physics principles to related high-weight IB HL exam topics. You will next explore conduction, convection and radiation as the three fundamental thermal energy transfer mechanisms, which builds directly on your understanding of radiative heat exchange between the Earth and its atmosphere. You can then progress to study the physics of climate mitigation strategies, including carbon capture technologies and low-carbon renewable energy generation, which are common 6-8 mark extended response topics in Paper 2 Section B. This content also transfers directly to the Astrophysics optional unit, where you will calculate equilibrium temperatures for exoplanets to assess habitability. Mastery of this sub-topic guarantees you almost all available marks for the greenhouse effect questions that appear in nearly every IB Physics HL exam cycle.

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