Question

is it possible for the floater to be neutrally buoyant at two different temperatures in the galileo thermometer?

Answer 1

Galileo thermometer works on the density change with respect to temperature and principle of buoyancy which determines whether objects float or sink in a liquid according to density of the liquid at different temperature. If an object weight is matched to the density of the liquid at a specific temperature, it will neither rise nor fall, which is called neutrally buoyant. If the temperature of the liquid changes, the density of the liquid also changes, and the objects floating in it will rise or sink accordingly so it is not possbile for a liquid to maintain same density at two temperature so if it is nuetrally buyont at one density and its corresponding temperature. when the temperature and corresponding density changes it cannot be nuetrally buoyant.

So Answer is No it is not possible.