IB · B · structured
The particulate nature of matter · Question 9
The particulate nature of matter · Original GioPhysics question with a detailed, mark-by-mark answer guide.
- Demand
- discriminating
- Marks
- 12
- Topics
- 1
- Answer
- Complete
The Earth may be modelled as a black body of average surface temperature 288 K. The Stefan–Boltzmann constant is 5.67 × 10⁻⁸ W m⁻² K⁻⁴.
- (a)
Calculate Calculate the power radiated per square metre by the Earth's surface at this temperature.
2 marks - (b)
Determine The average intensity of solar radiation absorbed by the Earth is 238 W m⁻². Determine the temperature the Earth's surface would have if it radiated only this absorbed power directly to space.
3 marks - (c)
Explain Explain, using your answers to (a) and (b), how the greenhouse effect accounts for the difference between 255 K and the observed 288 K.
4 marks - (d)
Discuss A student says that because the Earth's surface radiates 390 W m⁻² but absorbs only 238 W m⁻² from the Sun, energy is being created. Discuss this claim.
3 marks
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(a)
Calculate Calculate the power radiated per square metre by the Earth's surface at this temperature.
List the given quantities with units, identify the required quantity, write the governing relationship before substituting, and keep extra digits until the final line so rounding does not distort the result.
- 1
I = σT⁴ = 5.67 × 10⁻⁸ × 288⁴
- 2
I = 390 W m⁻²
(b)
Determine The average intensity of solar radiation absorbed by the Earth is 238 W m⁻². Determine the temperature the Earth's surface would have if it radiated only this absorbed power directly to space.
List the given quantities with units, identify the required quantity, write the governing relationship before substituting, and keep extra digits until the final line so rounding does not distort the result.
- 1
sets σT⁴ = 238
- 2
T⁴ = 238/5.67 × 10⁻⁸ = 4.20 × 10⁹
- 3
T = 255 K
(c)
Explain Explain, using your answers to (a) and (b), how the greenhouse effect accounts for the difference between 255 K and the observed 288 K.
State the outcome first, then link cause to effect with the relevant physical principle. Each link in the reasoning should be explicit enough to earn its own marking point.
- 1
the Earth's surface radiates in the infrared, at wavelengths determined by its temperature
- 2
greenhouse gases in the atmosphere absorb strongly in the infrared while remaining largely transparent to the incoming shorter-wavelength solar radiation
- 3
the absorbed energy is re-emitted in all directions, so a substantial part returns to the surface
- 4
the surface therefore receives energy from the Sun and from the atmosphere, and must warm to 288 K before it radiates 390 W m⁻² and reaches equilibrium
(d)
Discuss A student says that because the Earth's surface radiates 390 W m⁻² but absorbs only 238 W m⁻² from the Sun, energy is being created. Discuss this claim.
Build a chain of claim, evidence and physics reasoning. Address more than one relevant factor, identify a limitation or assumption, and finish with a conclusion that is conditional on the evidence rather than absolute.
- 1
the claim is wrong: it counts only one of the two sources of energy arriving at the surface
- 2
the surface also receives roughly 150 W m⁻² of infrared radiation emitted downward by the atmosphere, so the total input balances the 390 W m⁻² output
- 3
the atmosphere in turn radiates to space, and it is the top of the atmosphere — not the surface — where the 238 W m⁻² balance with space must hold
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