Ångström periodic heating method 2026-10-18
The Ångström periodic heating method measures thermal diffusivity by periodically heating one end of a rod and comparing the resulting temperature oscillations at two separated thermometers. The farther signal has a smaller amplitude and a later wave phase. Their combination measures how quickly the material redistributes heat, without requiring the absolute heater power. The method bears the name of Anders Jonas Ångström, the physicist who became a professor at Uppsala in 1858.[ref]
Anders Ångström by Uppsala University. Uppsala University, Anders Ångström: appointment to professor of physics in 1858
An actual teaching apparatus is PASCO's TD-8513: four metal bars share a heater/cooler using the thermoelectric effect, and each has two embedded thermistors about apart. Foam covers reduce environmental heat transfer. Its manual instructs students to measure sensor spacing and connect the thermistors through a temperature interface to a computer. For the aluminium bar, a – triangular drive is applied with a period. Recording begins after the amplitudes stabilize; two cycles provide amplitudes and the delay between corresponding peaks. Repeated runs at and test consistency. The manual converts the inferred thermal diffusivity to thermal conductivity using mass density and specific heat capacity.[ref]
Heat Conduction Apparatus TD-8513 Instruction Manual by PASCO scientific. PASCO scientific, Heat Conduction Apparatus TD-8513 Instruction Manual, p. 3 Introduction; pp. 9–11 Experiment 2: apparatus, amplitude/phase inference and aluminium procedure
For a general rod experiment, attach small thermocouples, thermistors or other thermometers at measured positions , record both against the same clock, and establish a steady periodic thermal state. A sinusoid is especially convenient. For a switched or triangular drive, isolate the same Fourier series component at both sensors: unrelated peaks in distorted waveforms need not measure that component's phase difference. Subtract each sensor's mean temperature; a steady spatial background does not belong in the oscillating amplitude ratio. Small excursions help keep thermal conductivity, mass density and specific heat capacity constant.
The appeal is that the rod supplies two complementary clocks: decreasing amplitude measures spatial damping, while increasing wave phase lag measures delay. Unlike laser flash analysis, which follows a transient after one pulse, this method repeatedly samples a steady periodic thermal state. The timing determines thermal diffusivity in . To infer thermal conductivity in , also measure or otherwise justify the mass density and specific heat capacity at constant pressure :Here the stationary-solid approximation neglects thermal expansion and mechanical work, as in thermal diffusivity. A timing measurement alone cannot distinguish two materials with the same and different volumetric heat capacities.
Regulated calibration bath 2026-10-18
A regulated bath holds its temperature near a chosen setting through feedback control, while stirring reduces internal temperature gradients. Its finite heat capacity buffers disturbances; external heating and cooling replace the ideal heat bath's unlimited capacity. This is useful for thermometer calibration and for maintaining a blackbody calibration source at a known temperature.
Joel B. Fowler's A Third Generation Water Bath Based Blackbody Source reports a NIST test of a stirred water bath containing a copper blackbody cavity. A bottom plate supplied heating and cooling; a double stirrer circulated water. Electronic feedback control regulated heating. An electronic thermometer with a thermistor probe provided the readout. The preparation was to approach a selected setting, wait for stabilization, adjust against the measured temperature and then log continuously.[ref]
A Third Generation Water Bath Based Blackbody Source by Joel B. Fowler. A Third Generation Water Bath Based Blackbody Source, §§2–3, printed pp. 592–593: bath construction, controller and setpoint procedure
To test spatial uniformity, one thermistor stayed near the cavity tip while another visited ten locations at three heights. The simultaneous reference distinguished spatial differences from temporal drift. An insulated dome reduced thermal conduction along probe casings. Table 1 reports nonzero departures at several settings: circulation did not make every location identical. The measurement uncertainty analysis separately included uniformity, stability, setting, immersion and readout contributions. These tests supported a bounded temperature assignment around the cavity, rather than infinite heat capacity or perfect thermal equilibrium throughout the apparatus.[ref]
A Third Generation Water Bath Based Blackbody Source by Joel B. Fowler. A Third Generation Water Bath Based Blackbody Source, §4.1 and Tables 1–2, printed pp. 594–595: fixed and movable probes, immersion control, measured nonuniformity and uncertainty components
Thermistor 2026-10-18
A thermistor is a temperature-sensitive resistor used as a resistance thermometer. Its calibrated electrical resistance supplies a temperature indication; probe heat capacity and unwanted thermal conduction can affect its response and immersion error.
