Bimetallic Spiral Thermometer

​
bimetal spiral components
active
Mg
Al
Ag
Cu
passive
Ti
Fe
Ni
Au
strip thickness
0.2
outside temperature (°C)
20
auto-calibrate
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
L
and strip thickness
s
is given by
ϕ=(
α
1
-
α
2
)(T-
T
0
)L/s
, where
α
1
and
α
2
are the coefficients of linear expansion of the component materials used.

Details

For the arc length of Archimedes's spiral, we use the classical formula (Wolfram|Alpha)
L=2nπ(s+g)
1+4
2
n
2
π
+arcsinh(2nπ)
,
where
g
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
2π
at 60 °C.
Snapshot 1: a very sensitive bimetal Mg/Ti with thermal expansion coefficients of 26/8.6
-6
10
-1
°C
Snapshot 2: a less sensitive bimetal Cu/Ni with thermal expansion coefficients of 17/13
-6
10
-1
°C
Snapshot 3: the uncalibrated version of Snapshot 2
For extensive information about bimetals, see "Thermostatic Bimetal Handbook" from Kanthal AB, Sweden.

External Links

Archimedean Spiral (Wolfram MathWorld)

Permanent Citation

Erik Mahieu
​
​"Bimetallic Spiral Thermometer"​
​http://demonstrations.wolfram.com/BimetallicSpiralThermometer/​
​Wolfram Demonstrations Project​
​Published: December 5, 2011