Describe experiments to distinguish between good and bad absorbers of infrared radiation

2.3.3 Radiation

Objective

Describe and analyse simple experiments that allow students to distinguish between good and bad absorbers of infrared (IR) radiation, and relate the observations to the qualitative form of the Stefan‑Boltzmann relationship ( P ∝ T⁴ ).

Key Concepts

• Infra‑red radiation is the part of the electromagnetic (EM) spectrum with wavelengths roughly 0.7 µm – 1000 µm. (See the EM‑spectrum diagram below.)
• All bodies emit IR radiation. The emitted power increases rapidly with temperature and with the emitting surface area.
• Black‑body – an idealised surface that absorbs all incident radiation (absorptivity α = 1) and therefore emits the maximum possible IR at a given temperature.
• Real surfaces have an emissivity ε (0 ≤ ε ≤ 1) that is equal to their absorptivity (Kirchhoff’s law) for opaque materials.
• Good absorber ≈ high α (≈ 1) → also a good emitter (high ε).
  

  Bad absorber ≈ low α (≈ 0) → also a poor emitter (low ε).

• Qualitative Stefan‑Boltzmann relationship

  \[

  P\;\propto\;\varepsilon\,A\,T^{4}

  \]

  where P is the radiated power, A the emitting area and T the absolute temperature (K). The constant σ is not required at IGCSE level; only the fourth‑power dependence on T and the linear dependence on A are needed.

• Surface colour/texture influences α and ε:

  • Matte black → α ≈ 1, ε ≈ 0.9 – 1 (good absorber/emitter).
  • Matte white or shiny metal → α ≈ 0.1 – 0.3, ε ≈ 0.1 – 0.3 (poor absorber/emitter).

Theoretical Background

Black‑body vs. Real Surfaces

• A perfect black‑body absorbs 100 % of incident radiation at all wavelengths and emits according to P ∝ T⁴.
• Real surfaces have an emissivity ε < 1; the radiated power is reduced by the factor ε.
• Kirchhoff’s law (for opaque bodies) states α = ε, so a surface that is a good absorber is also a good emitter.

Emissivity (ε) and Absorptivity (α)

• Typical values (room temperature):

  • Matte black paint ≈ 0.95
  • Polished aluminium ≈ 0.03
  • Matte white paint ≈ 0.10

• In the temperature range used for IGCSE experiments (≈ 300–400 K) ε is effectively constant.

Temperature and Area Dependence

• Doubling the absolute temperature increases radiated power by a factor of 2⁴ = 16.
• Doubling the emitting area doubles the radiated power (P ∝ A).

Radiation in the Context of Other Heat‑Transfer Modes

• Conduction – transfer through direct contact; depends on material conductivity and temperature gradient.
• Convection – transfer by moving fluid (air or water); depends on fluid motion and temperature difference.
• Radiation – transfer by EM waves; does not require a material medium and can occur across a vacuum.
• In many everyday situations (e.g., a hot cup of tea), all three modes act together; the experiments below isolate radiation by minimising conduction and convection.

Supplementary Point (optional for deeper study)

For fluids, the pressure increase with depth is given by Δp = ρgΔh. Although not required for the core IGCSE radiation content, it may appear in extended questions linking pressure and temperature.

Experimental Set‑ups

1. Comparing a Good and a Bad IR Absorber

Two identical aluminium plates are painted matte black (good absorber) and matte white (bad absorber) and exposed to the same IR source.

1. Apparatus

   • Two 10 cm × 10 cm × 0.5 cm aluminium plates; one matte black, one matte white.
   • Infra‑red lamp (≈ 100 W) with a constant‑voltage supply.
   • Two identical thermocouples or digital temperature probes (±0.1 °C) attached to the rear faces with thermal paste.
   • Insulating stand that holds the plates parallel, 10 cm from the lamp, and prevents heat conduction between them.
   • Stopwatch, data‑logging sheet or computer interface.

2. Procedure

   1. Record the ambient temperature (T₀) with both probes.
   2. Switch on the IR lamp and start the timer.
   3. Record the temperature of each plate every 30 s for 5 min (heating phase).
   4. Switch off the lamp and continue recording every 30 s for a further 5 min (cooling phase).
   5. Repeat the whole run twice to estimate random error.

3. Typical Data (°C)

   Time (s)	Black Plate	White Plate
   0	20.0	20.0
   30	35.2	28.5
   60	45.8	34.1
   120	58.3	42.7
   180	62.5	45.9
   240	64.0	46.8
   300	64.5	47.0
   360 (cooling)	63.0	46.5
   420	61.2	45.8
   480	59.0	44.9

4. Analysis

   • Plot temperature vs time for each plate. The steeper slope during heating (and cooling) of the black plate shows a larger net radiative power.
   • Determine the equilibrium temperature (where heating and cooling rates balance). Approximate values:

     Teq(black) ≈ 64 °C, Teq(white) ≈ 47 °C.

   • Using the proportional form of the Stefan‑Boltzmann law,

     \[

     \frac{\varepsilon{\text{black}}}{\varepsilon{\text{white}}}

     \approx

     \frac{T{\text{black}}^{4}-T{0}^{4}}{T{\text{white}}^{4}-T{0}^{4}}

     \]

     (area cancels). Inserting the measured temperatures (in K) gives a ratio ≈ 9, consistent with εblack ≈ 0.95 and εwhite ≈ 0.10.

   • Uncertainty considerations

     • Thermometer uncertainty ± 0.1 °C → propagate to power using \(\Delta P/P \approx 4\Delta T/T\).
     • Thermal contact resistance – minimise with a thin layer of thermal paste.
     • Air currents affect cooling; repeat in a draught‑free room.

5. Conclusion

   The matte‑black plate is a good IR absorber (and emitter), reaching a higher steady‑state temperature and cooling more rapidly than the matte‑white plate, which is a poor absorber.

2. Transmission/Absorption of IR Through Different Materials

Measuring how much IR passes through a sample indicates whether the material is a good absorber (low transmission) or a poor absorber (high transmission).

1. Apparatus

   • Broad‑band IR source (e.g., a heated nichrome filament at ≈ 150 °C).
   • Thermopile detector with a digital voltmeter (sensitivity ≈ 10 µV · W⁻¹).
   • Sample holder that places a flat sheet directly between source and detector.
   • Samples (≈ 5 cm × 5 cm): matte black cardboard, aluminium foil, clear glass, transparent plastic film.

2. Procedure

   1. Zero the voltmeter with no sample in place; record the baseline voltage V₀ (proportional to incident intensity I₀).
   2. Insert a sample, wait 10 s for thermal equilibrium, record the voltage V.
   3. Repeat three times per sample and compute the mean and standard deviation.
   4. Calculate the transmission fraction \(\tau = I/I{0} = V/V{0}\).

3. Typical Results

   Sample	Mean Voltage (mV)	Transmission τ
   Black cardboard	0.12 ± 0.01	0.05
   Aluminium foil	0.09 ± 0.01	0.04
   Clear glass	0.85 ± 0.02	0.70
   Plastic film	0.78 ± 0.02	0.65

4. Analysis

   • Materials with τ < 0.1 absorb most of the incident IR → good absorbers.
   • Materials with τ > 0.6 transmit most IR → poor absorbers.
   • Uncertainty propagation: \(\displaystyle \frac{\sigma_{\tau}}{\tau}

     \approx \sqrt{\left(\frac{\sigma_{V}}{V}\right)^{2}

     +\left(\frac{\sigma{V{0}}}{V_{0}}\right)^{2}}\).

5. Conclusion

   Matte black cardboard and aluminium foil are good IR absorbers, whereas clear glass and plastic film are bad absorbers because they allow most IR to pass through.

Everyday Applications

Safety Considerations

• IR lamps become very hot – handle plates with heat‑resistant gloves or tongs.
• Do not look directly at the lamp; wear protective goggles for high‑intensity sources.
• Secure all electrical connections and inspect cables before each session.
• If a vacuum chamber is used (extension question), ensure it is rated for the temperature and that all seals are intact.

Extension Questions

1. How would the temperature‑time curves change if the experiment were performed in a vacuum chamber where convection is eliminated?
2. Explain why a polished metal surface looks shiny (high reflectivity in the visible) yet can be a good absorber of IR radiation.
3. Design an experiment to determine the emissivity of an unknown material using the Stefan‑Boltzmann relationship and a calibrated black‑body reference.
4. Discuss how the greenhouse effect illustrates the role of good IR absorbers in the atmosphere.