I’d love to build a Galileo thermometer, but I haven’t been able to find any detailed information on how to make one. So, I created my own design for the project.
However, I have some uncertainties and possible small errors in my approach. In the last photo I’ve attached, you’ll find my specific questions and doubts about the construction process.
If anyone could take a look and share their insights, I’d really appreciate it.
It sounds like your problem is essentially
"How do I choose the quantity of materials to use in each sphere"
First you need to understand how the thermometer works. The density of the fluid in the large vessel will change with temperature. The balls within it will have a range of constant densities. As the temperature changes, some balls will float, and others will not. This allows you to deduce the temperature.
Technically this might still work if the balls do change in density with temperature, as long as they don't change as much as the suspending fluid, but the calculations will be more complicated. Lets assume instead that the balls are non-compressible and do not change in density with temperature.
First make a chart of density vs temperature for the suspending fluid. The curve is not linear for water as you get close to zero, so depending on the operating range you may want to use a different fluid or a mix of them.
Each of the balls will have a temperature written on it, the balls density should match the suspending fluid at that temperature. Above this temp it will float, below it will sink.
Measure the volume of each ball by liquid displacement. Multiply the volume by the target density to get the target mass.
Use a very accurate scale and construct the balls by any method or filling, so long as the resulting mass is correct.
If the ball is non-compressible, it doesn't matter what's inside of it. It only matters what the volume is, and what it weights. (aka it's density).
