# Greenhouse effect

> IB Physics SL · IB Physics 2023 SL Syllabus
> Source: https://www.owlsprep.com/study/ib-physics-sl-u2-greenhouse-effect/

This module explains the physical mechanism of the natural greenhouse effect, key greenhouse gases, albedo impacts, equilibrium temperature calculations, and the difference between natural and anthropogenic enhanced warming.

**Prerequisites:** [Black body radiation and Stefan-Boltzmann law](https://www.owlsprep.com/study/ib-physics-sl-u2-black-body-radiation/); [Basic thermal energy transfer modes](https://www.owlsprep.com/study/ib-physics-sl-u2-thermal-energy-transfer/)

## Learning objectives

- Identify primary natural and anthropogenic greenhouse gases and their sources
- Explain the physical mechanism of longwave infrared radiation absorption by atmospheric gases
- Calculate Earth's theoretical equilibrium temperature with and without the natural greenhouse effect
- Distinguish between the natural greenhouse effect and anthropogenic enhanced greenhouse effect

## Core Mechanism of the Natural Greenhouse Effect

The natural greenhouse effect is a critical process that keeps Earth's surface warm enough to support liquid water and life. Without it, the average surface temperature would be well below the freezing point of water.

**Natural Greenhouse Effect** — The process where atmospheric greenhouse gases absorb outgoing longwave infrared radiation emitted by the Earth's surface, re-radiating a portion of that energy back towards the surface rather than letting it escape directly to space.

> **info**
>
> Incoming solar radiation is mostly shortwave visible light, which passes through the atmosphere almost completely unabsorbed before being absorbed by the land and oceans.

**Worked example:** Identify which of the following radiation types is absorbed by greenhouse gases: 400 nm visible light, 10 μm infrared radiation, 200 nm ultraviolet radiation.

1. First, recall the peak wavelength of radiation emitted by the Earth's ~290 K surface using Wien's displacement law.
2. $$\lambda_{\text{peak, Earth}} = \frac{2.9 \times 10^{-3} \, \text{m K}}{290 \, \text{K}} = 10 \, \mu\text{m}$$
3. Greenhouse gases are transparent to visible and most UV radiation, so they only absorb the 10 μm infrared radiation.

**Check your understanding**

Test your understanding of the basic mechanism:

1. What type of radiation do greenhouse gases primarily absorb?

   - Incoming shortwave UV
   - Outgoing longwave infrared
   - Incoming visible light
   - Outgoing gamma radiation

   *Why:* Greenhouse gases do not absorb most incoming solar radiation, only the longer wavelength radiation re-emitted from the warm Earth surface.

## Key Greenhouse Gases and Absorption Properties

The four most important greenhouse gases for Earth's climate are water vapour, carbon dioxide, methane, and nitrous oxide. Each has distinct absorption bands in the infrared spectrum and different atmospheric lifetimes.

| Greenhouse Gas | Primary Natural Source | Primary Anthropogenic Source | Atmospheric Lifetime |
| --- | --- | --- | --- |
| Water vapour (H₂O) | Evaporation from oceans | Combustion of fossil fuels | ~10 days |
| Carbon dioxide (CO₂) | Volcanic eruptions, respiration | Fossil fuel combustion, deforestation | ~100 years |
| Methane (CH₄) | Wetland decomposition | Livestock, landfill, natural gas leaks | ~12 years |
| Nitrous oxide (N₂O) | Soil bacterial activity | Agricultural fertilisers | ~120 years |

> **tip**
>
> You do not need to memorise exact absorption wavelengths, but you should know that CO₂ and water vapour are responsible for over 95% of the total natural greenhouse warming.

> **Exam tip**
>
> IB exam questions very often ask you to explain why nitrogen and oxygen are not classified as greenhouse gases, so make sure you can reference their symmetric diatomic structure and lack of vibrational dipole change.

## Equilibrium Temperature Calculations

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

*Starting from:* Total incoming solar power equals total power radiated by Earth as a black body

1. Total solar power incident on Earth's cross-sectional area: $P_{\text{in}} = S \times \pi R^2 \times (1-\alpha)$
2. Total power radiated from Earth's full spherical surface via Stefan-Boltzmann law: $P_{\text{out}} = \sigma T^4 \times 4 \pi R^2$
3. Cancel common terms and rearrange to solve for T:
4. $$T = \left( \frac{S(1-\alpha)}{4 \sigma} \right)^{1/4}$$

*Conclusion:* For S=1360 W m⁻², α=0.3, this gives T ≈ 255 K (-18 °C), far below the actual average surface temperature of 288 K (15 °C). The 33 K difference is the natural greenhouse effect warming.

**Worked example:** Calculate the new equilibrium temperature if the average albedo of Earth decreases from 0.3 to 0.25 due to melting sea ice.

1. Substitute the new albedo value into the equilibrium temperature formula:
2. $$T = \left( \frac{1360 \times (1-0.25)}{4 \times 5.67 \times 10^{-8}} \right)^{1/4}$$
3. Simplify the numerator and denominator inside the brackets:
4. $$T = \left( \frac{1020}{2.268 \times 10^{-7}} \right)^{1/4} = (4.497 \times 10^9)^{1/4} \approx 259 \, \text{K}$$
5. Convert to Celsius for the final answer: 259 K - 273 = -14 °C, a 4 K increase from the original no-atmosphere value.

*Calculator:* allowed

## Enhanced Greenhouse Effect and Exam Phrasing

The enhanced greenhouse effect describes the additional warming caused by human activities increasing atmospheric greenhouse gas concentrations beyond pre-industrial levels, leading to a rise in average global surface temperatures.

**Exam command terms**

IB Physics uses specific command terms for greenhouse effect questions, with defined marking expectations:

- **Outline** — Give a brief, clear summary of the mechanism, no extra detail required

- **Explain** — You must reference shortwave vs longwave radiation, and the re-radiation back to the surface to get full marks

- **Calculate** — Show full working for the equilibrium temperature formula, including units at each step

## Common pitfalls

- **Wrong:** Stating that greenhouse gases absorb incoming shortwave solar radiation
  - Why it fails: Almost all incoming solar radiation is shortwave visible light, which passes unabsorbed through the atmosphere to reach the surface
  - Correct: Explicitly state that greenhouse gases only absorb outgoing longwave infrared radiation re-emitted by the Earth's warm surface
- **Wrong:** Claiming the natural greenhouse effect is a harmful, human-caused process
  - Why it fails: The natural greenhouse effect is a necessary, life-supporting process that has existed in Earth's atmosphere for billions of years
  - Correct: Reserve the term 'enhanced greenhouse effect' exclusively for the anthropogenic additional warming from human activity
- **Wrong:** Using the full surface area of the Earth when calculating incoming solar power
  - Why it fails: Solar radiation only hits the cross-sectional circular area of the Earth, not the full 4πR² spherical surface
  - Correct: Use πR² for incoming power, and 4πR² for total outgoing radiated power in equilibrium calculations
- **Wrong:** Including nitrogen (N₂) as a major greenhouse gas
  - Why it fails: Symmetric diatomic molecules with no dipole moment change during vibration cannot absorb infrared photons
  - Correct: Only list polyatomic molecules like CO₂, H₂O, CH₄ and N₂O as primary greenhouse gases
- **Wrong:** Forgetting to convert temperature from Kelvin to Celsius in final answers
  - Why it fails: IB mark schemes almost always expect final surface temperature values to be stated in degrees Celsius for climate-related questions
  - Correct: Always subtract 273 from your Kelvin result to give the temperature in °C unless explicitly told otherwise

## Cheatsheet

| Quantity | Formula | Units | Key Value |
| --- | --- | --- | --- |
| Solar constant S | Measured at top of atmosphere | W m⁻² | 1360 |
| Earth average albedo α | Dimensionless reflectivity | Unitless | 0.3 |
| No-greenhouse equilibrium temp | $T = \left( \frac{S(1-\alpha)}{4\sigma} \right)^{1/4}$ | K | 255 K (-18 °C) |
| Actual average surface temp | Measured global average | °C | 15 °C (288 K) |
| Natural greenhouse warming | Difference between actual and no-greenhouse temp | K | 33 K |

## What's next

Mastering the greenhouse effect gives you a foundational understanding of atmospheric energy balance that is tested in almost every IB Physics SL exam session. This concept directly connects to real-world climate physics questions that frequently appear in Paper 2 data analysis sections. You will next apply these calculation skills to albedo variation scenarios, before moving on to explore the physics of climate mitigation strategies including carbon capture and renewable energy thermal systems. This knowledge also overlaps with content from your IB Environmental Systems and Societies course, helping you cross-reference concepts across your subject portfolio.

---

From [OwlsPrep](https://www.owlsprep.com) — free study guides for A-Level, IB, AP and IGCSE, written against the official syllabus. Canonical page: https://www.owlsprep.com/study/ib-physics-sl-u2-greenhouse-effect/