SOL 101 › Lab

Lab 101-C — Filament Temperature from a Light Bulb

Goes with: Unit 5. Time: 2 hours. Cost: about \(50–\)100 (estimate; the bench supply is reused in many later labs).

Goal

Measure a small incandescent bulb's voltage and current from glowing dull red to full brightness, use the resistance–temperature behaviour of tungsten to estimate the filament temperature, and connect colour and power to Planck's and Stefan–Boltzmann's laws.

What you will learn

Shopping list

Item Spec / example Qty Approx. cost (estimate) Where
Adjustable DC bench power supply 0–30 V, 0–5 A with V and A displays (e.g., Korad KA3005D or Eventek KPS305D class) 1 $50–90 Amazon
Small incandescent bulbs automotive #194 (≈ 14 V, 0.27 A) and/or #1156 (≈ 12.8 V, ~2 A) with sockets/pigtails 3–4 $5–10 auto-parts store, Amazon
Second multimeter to measure current and voltage independently of the supply's displays 1 $20–30 Amazon
Leads with alligator clips — 1 set $8 Amazon
Thermometer (room temperature) any 1 — household
Optional lux meter — 1 $20–30 Amazon

Safety

Background: resistance as a thermometer

Tungsten's resistivity rises roughly 15-fold from room temperature to ~3000 K. Tabulated data (CRC Handbook) are well approximated, for this lab, by

\[\frac{R(T)}{R_{300}} \approx \left(\frac{T}{300\ \text{K}}\right)^{1.2} \quad \Rightarrow \quad T \approx 300\ \text{K} \times \left(\frac{R}{R_{300}}\right)^{1/1.2}\]

This fit is our approximation (good to roughly ±10 % in temperature over 300–3000 K). For better accuracy, interpolate directly in the CRC resistivity table.

Procedure

  1. Cold resistance. Measure \(R_\text{cold}\) with the multimeter's ohm range (subtract lead resistance by touching leads together). Better: use the supply at a tiny current (e.g., 10 mA) where the filament does not warm: \(R = V/I\). Record room temperature \(T_0\); correct to 300 K if needed.
  2. Connect the supply in constant-voltage mode with the second meter in series (current). Increase voltage in steps: 0.1, 0.2, 0.5, 1, 2, 3 … up to rated voltage.
  3. At each step wait 10 s, record \(V\), \(I\), colour seen (none / dull red / orange / yellow / white), and optional lux.
  4. Repeat for a second bulb type.

Analysis

  1. Compute \(R = V/I\) and \(P = VI\) for each step.
  2. Estimate \(T\) from \(R/R_{300}\).
  3. Plot \(\log P\) against \(\log T\). Radiation dominates at high temperature, so the slope should approach 4 (Stefan–Boltzmann). At low temperatures conduction through the leads and gas cooling lower the slope.
  4. Compute the Wien peak \(\lambda_\text{max} = 2.898\times10^{-3}/T\) at full voltage and plot the Planck curve for that temperature against the visible band (Unit 5 code).
  5. Compare the colour you saw with the Planck curve: first visible glow is dull red around ~800–900 K (Draper point ≈ 798 K).

Expected results

How to interpret

The experiment shows directly that thermal emission is mostly IR at filament temperatures, explaining why halogen lamps are poor solar simulators and why the ~5800 K Sun is so much bluer. The \(T^4\) law is why a modest temperature increase in a furnace or on the Sun's surface changes emitted power dramatically — and why radiative heat transfer dominates in crystal-growth hot zones (SOL 301).

Sources

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