IB Physics SL B.1.14 Black-Body Radiation

Practise applying the Stefan-Boltzmann law to spherical emitters, comparing radius and temperature effects and extracting the fourth-power relationship from data or logarithmic…

Exam points

calculate emitted power with L = σAT⁴ and use A = 4πR² for a spherical source
compare two radiators by forming a radius-squared and temperature-fourth-power ratio
linearise Stefan-Boltzmann data so a log-log gradient near four tests the T⁴ dependence

[Maximum number: 4]

This question is in two parts. Part 1 is about solar radiation and the greenhouse effect. Part 2 is about a mass on a spring.

Part 1 Solar radiation and the greenhouse effect
The following data are available.

Table for Question B.1.14—Black-body radiation question 1 — IB Physics SL

(a)

State the Stefan-Boltzmann law for a black body.

[ 2 ]

(b)

The average power absorbed per unit area at the Earth's surface is $240 \mathrm{Wm}^{-2}$ . By treating the Earth's surface as a black body, show that the average surface temperature of the Earth is approximately 250 K .

[ 2 ]

power radiated=power absorbed;
$T=\sqrt[4]{\frac{240}{5.7 \times 10^{-8}}}(=250 \mathrm{~K}) ;$

Marking guidance:

Accept answers given as 260 (K).

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B.1.14—Black-body radiation question 1

Question (a)

Question (b)