IB Physics SL B 2 2 Emissivity Questions

Practise IB Physics SL B.2.2 by relating emissivity to emitted intensity, black-body spectra and planetary energy balance.

Exam points

Interpret emissivity as radiation intensity relative to a black body and compare surfaces using the Stefan–Boltzmann law and peak-wavelength information.
Derive a planet’s equilibrium-temperature relation by balancing absorbed solar power, including albedo, with its emitted thermal radiation.
Calculate Earth’s surface temperature with and without atmospheric back-radiation using the emissivity of the surface and atmosphere.
Determine atmospheric re-radiation towards the surface from the emitted intensity and the outgoing radiation balance.

[Maximum number: 3]

The diagram shows a simplified energy-balance model for the Earth surface–atmosphere system.

Figure for Question IB Physics SL B 2 2 Emissivity Questions question 1 — IB Physics SL

The following data are given:

\begin{aligned} \text { Average albedo of Earth } & =0.30 \\ \text { Average global temperature of the surface } & =288 \mathrm{~K} \\ \text { Average Earth-Sun distance } & =1.5 \times 10^{11} \mathrm{~m} \end{aligned}

Determine the average intensity re-radiated by the atmosphere towards the surface. Assume that the emissivity of the surface is 0.90 .

Emitted intensity $=5.67 \times 10^{-8} \times 0.90 \times 288^{4}\approx351 \mathrm{~W} \mathrm{~m}^{-2}$

Intensity leaving Earth $=238 \mathrm{~W} \mathrm{~m}^{-2}$

Re-radiated intensity $=351-238=113 \mathrm{~W} \mathrm{~m}^{-2}$

Marking guidance:

Ignore units as they are not required for the answer.
The steps in the calculation must be
checked.
Accept outgoing intensity $=240 \mathrm{~W}$ $m^{-2}$ for MP2.

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IB Physics SL B 2 2 Emissivity Questions question 1