IB Diploma Physics · topic B.2
Greenhouse effect
Connect the ideas, make your working visible, and test the result. Use the hints when you need a starting point; open the full solution after your attempt.
Extra challenging questions
Work through the linked stages and explain what each result means.
A planet's energy balance with an albedo feedback
A planet receives stellar irradiance 1360 W m⁻² on a surface perpendicular to incoming light. Its albedo is initially 0.30. Assume a spherical planet and uniform effective emission σT⁴, where σ = 5.67×10⁻⁸ W m⁻² K⁻⁴. The supplied graph gives emitted flux for several effective temperatures. The actual surface is warmer than this simple emission temperature. Supplied data (Temperature / K; Emitted flux / W m⁻²): (240, 188.117), (255, 239.742), (270, 301.327), (288, 390.079). (a) Calculate globally averaged absorbed stellar flux and equilibrium effective temperature, explaining the factor of four. [3 marks] (b) Albedo drops to 0.25. Find the new absorbed flux and temperature, and distinguish the greenhouse mechanism from the albedo change. [3 marks]
Blackbody emitted flux
Supplied question data. Read the labelled axes and use the observations to test the physical model.
Vertical axis (y): Emitted flux / W m⁻²
Horizontal axis (x): Temperature / K
Read the exact data as a table
| Temperature / K | Emitted flux / W m⁻² |
|---|---|
| 240 | 188.117 |
| 255 | 239.742 |
| 270 | 301.327 |
| 288 | 390.079 |
These are the supplied values, not a worked answer. No fitted trend is drawn.
Show a hint
Begin with part (a): Calculate globally averaged absorbed stellar flux and equilibrium effective temperature, explaining the factor of four.
Reveal the worked solution
- The planet intercepts light over a disc πR² but emits across a spherical area 4πR², so averaged incoming irradiance is S/4.
- Absorbed flux is (1−0.30)(1360)/4 = 238 W m⁻².
- Equilibrium requires σT⁴ = 238, giving T = (238/σ)¹/⁴≈254.6 K. This is the effective emission temperature, not automatically the surface temperature.
- With albedo 0.25, absorbed flux is 0.75(1360)/4 = 255 W m⁻², an increase of 17 W m⁻².
- New equilibrium temperature is (255/σ)¹/⁴≈259 K, about 4.4 K above the initial effective temperature.
- Albedo changes reflected incoming light. Greenhouse gases absorb and emit outgoing infrared radiation and alter energy transfer between surface and atmosphere. Melting reflective ice can lower albedo and reinforce warming; this simple model does not quantify the complete coupled climate response.
Answer (a) Absorbed flux = 238 W m⁻²; effective temperature≈254.6 K. (b) New flux = 255 W m⁻²; effective temperature≈259 K; lower albedo gives warming in this model.
Compare the assumptions, method and units with your attempt. Explain any correction before trying another question.