IB Physics SL B.2.2 Emissivity

Practise using emissivity as a surface's radiated intensity relative to a black body, combining εσT⁴ with albedo and energy balance to calculate temperature or emission.

Exam points

calculate emitted intensity as εσT⁴ with absolute temperature and dimensionless emissivity
compare two equal-intensity surfaces by combining Wien's law with the T⁴ dependence
derive equilibrium temperature by setting absorbed solar intensity equal to emitted εσT⁴

[Maximum number: 3]

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

Figure for Question B.2.2—Emissivity 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 $=\ll 5.67 \times 10^{-8} \times 0.90 \times 288^{4}=>351 \mathrm{~W} \mathrm{~m}^{-2}$

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

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

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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B.2.2—Emissivity question 1