Bimetallic Spiral Thermometer

This Demonstration simulates a classical bimetallic spiral thermometer (dial or coil thermometer).
An Archimedes's spiral made of a coiled bimetal strip gives a deflection proportional to the surrounding temperature and can serve as a thermometer.
The angular deflection of a bimetal spiral of length and strip thickness is given by , where and are the coefficients of linear expansion of the component materials used.

SNAPSHOTS

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DETAILS

For the arc length of Archimedes's spiral, we use the classical formula (Wolfram|Alpha)
,
where is the gap.
The thermometer is by default calibrated for the Mg/Fe bimetal. Other bimetal settings need to be calibrated individually. To do this, we insert a linear factor cal60, computed with Mathematica's built-in function FindRoot, to give a deflection of at 60 °C.
Snapshot 1: a very sensitive bimetal Mg/Ti with thermal expansion coefficients of 26/8.6
Snapshot 2: a less sensitive bimetal Cu/Ni with thermal expansion coefficients of 17/13
Snapshot 3: the uncalibrated version of Snapshot 2
For extensive information about bimetals, see "Thermostatic Bimetal Handbook" from Kanthal AB, Sweden.
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