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Is it possible to create a Galileo thermometer by hand with house hold items? What are the physics and mathematics behind the Galileo thermometer and how can I solve them to use different densities of liquids?

I want to attempt to create a Galileo thermometer (or a few if possible) as a science project that uses various liquids that have different densities at specific temperatures. I understand the fundamentals of how the thermometer works and at this point I am stuck at how to accurately adjust the weights on each globe to effect their temperature reading. Is there a formula for dealing with this? Or is the liquids in the globes different per globe and that is what makes them float or sink inside the main liquid and not the weight of the tag?

Any information would be appreciated.

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  • $\begingroup$ juliantrubin.com/encyclopedia/physics/galileo_thermometer.html not sure if it's too basic for you or if you have already read it. $\endgroup$
    – user108787
    Sep 23 '16 at 0:47
  • $\begingroup$ The effective density is (mass of float + mass of tag)/(volume of float + volume of tag). Since the tag is a more dense material, you just have to start with it too heavy and trim (or file) it until it has neutral buoyancy at a desired temperature.The globes are sealed, so their mass and volume are fixed $\endgroup$ Sep 23 '16 at 1:02
  • $\begingroup$ Oops, I hit ENTER. The volume of the float also will change due to thermal expansion. The thermometer won't work if the liquid and float have the same coefficient of expansion. $\endgroup$ Sep 23 '16 at 1:15
  • $\begingroup$ @KeithMcClary Is there a way to calculate the desired and/or approximate mass for the tag, or is this trial and error? $\endgroup$
    – jdoe
    Sep 23 '16 at 2:04
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If
$M =$ mass of float
$V = $volume of float
$m =$ mass of tag
$\rho =$ density of tag
$D =$ density of liquid
then $$D =\frac{M + m}{V+m/\rho} $$

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