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• Kristjan Salev

# HOW DOES A GALILEO THERMOMETER WORK, AND HOW TO READ IT

Updated: Jul 20, 2023

Galileo's thermometer is an ingenious device for measuring temperatures that looks a bit different than regular thermometers. Although it is named after the famous astronomer Galileo Galilei, Galileo himself did not build such a thermometer. However, Galileo discovered the principle on which the work of such a thermometer is based - the density of a liquid depends on its temperature. The first such thermometer was built in 1660, twenty years after Galileo's death.

The Galileo thermometer consists of a closed glass cylinder filled with a transparent liquid. Inside the liquid are smaller glass containers filled with different colored liquids, with small metal plates with different weights hanging below. Depending on the ambient temperature, the liquid inside the Galileo thermometer has a different density. At different liquid densities, the small containers also have buoyant forces of different magnitudes affecting them, allowing us to determine the temperature of the liquid (and the temperature of the surrounding air).

## What is buoyant force?

The buoyant force is an upward force acting on a body in a fluid. This force acts on the body when the body is partly in the liquid or when it is completely immersed in the liquid. It opposes the downward gravitational force, and its magnitude determines whether the body sinks, floats, or rises when submerged in liquid.

The magnitude of the buoyant force (Fb) is equal to the product of the density of the liquid (ρ), the volume (V) of the liquid displaced by the body, and the acceleration due to gravity (g). The force (Fg) with which the earth attracts the body is called the weight of the body and is equal to the product of its mass (m) and acceleration due to gravity (g).

If the buoyant force acting on a container with a colored liquid is more significant than its weight (Fb>Fg), the container will rise to the surface of the liquid. If the buoyant force on the container is equal to its weight (Fb=Fg), the container floats inside the liquid, and if it is less than its weight (Fb<Fg), the container sinks.

It is also important to note that the magnitude of the upward force acting on a small container in a thermometer does not depend on how deep the container is. It depends only on the overall density of the container and metal plate, and the density of the liquid in which they are submerged.

## What liquid is used in the Galileo thermometer?

The Galileo thermometer works on the principle that as the temperature of a liquid changes, so does its density. When the temperature changes, the liquid either expands or shrinks. When it heats up, its volume becomes larger, but the mass remains the same, and this means that the density must become smaller because the density is inversely proportional to the volume (ρ=m/V). However, when it cools, it contracts, and the same mass is contained in a smaller volume, which means that its density is higher.

The liquid inside the thermometer is some kind of alcohol (usually ethanol) because it has a significantly higher expansion factor than, for example, ordinary water. If it expands and shrinks more when the temperature fluctuates, then its density also changes within larger limits, and it is more convenient to measure the temperature with it.

## Different color vessels have different weights

Smaller vessels inside the thermometer mostly contain water colored with food coloring. Whether the colored liquid in the small container expands as it warms or contracts, as it cools, does not affect the thermometer's performance. They are colored to represent a certain temperature. Red usually represents warmer temperatures, and blue colder temperatures, while the rest of the colors (yellow, green, purple) are left in between.

How much a container with a colored liquid weighs depends primarily on the weight of the metal tag attached to it. Different colored containers have slightly different weights attached to them.

We can observe that the two containers in the top picture have slightly different weights attached to them. The yellow container with the metal tag has a mass of m1, and the blue container has a mass of m2. Since the yellow container has risen to the surface of the liquid, and the blue container is floating in the liquid, it means that in the first case, the buoyant force is greater than the weight of the container. In the second case, the buoyant force is equal to the weight of the container.

Similarly, since the mass of the yellow container and its metal label is less than that of the blue one, its density is also less. We can see that the temperature of the liquid in the thermometer in the upper picture is approximately 22 degrees Celsius. At this temperature, the density of the liquid in the thermometer is about the same as the blue container with the metal label because it is currently fully submerged but floating in the liquid.

## How to read a Galileo thermometer?

Measuring the temperature with the Galileo thermometer is quite convenient when one small container is submerged and floats in the middle of the thermometer, while some vessels have risen to the surface and some have sunk to the bottom. In this case, the temperature of the liquid, and therefore the temperature of the air surrounding the thermometer, is approximately the temperature indicated on the metal label of that container. It can be in degrees Fahrenheit or Celsius, depending on the thermometer.

If the temperature is low, then the density of the liquid is also higher, and all vessels float to the top of the thermometer. In this case, we can only say that the temperature is lower than indicated on the label on the lowest floating container.

If the temperature is high enough, the density of the liquid is low, and all containers sink to the bottom of the thermometer. In this case, we can only say that the temperature is higher than what is indicated on the label of the highest container.

At some temperatures, however, some containers are at the top, and some are at the bottom of the thermometer. In this case, the temperature is the average of the temperatures shown on the lowest container in the upper group and the uppermost container in the lower group. In the picture below it is, for example, 19 degrees ((20+18)/2).

## How accurate is Galileo thermometer?

The accuracy of the Galileo thermometer primarily depends on how well the weights are calibrated and how many colored vessels are in the thermometer. Smaller ones usually contain five vessels and measure temperature in a narrower range of 16-24 °C or 18-26 °C. Larger ones with ten vessels can measure temperature in a wider range of 16-34°C. Temperatures below the minimum and above the maximum are therefore not measurable which is why this thermometer is suitable for indoor use. Since the temperatures are usually marked every two degrees, and there is not always one container floating in the center of the thermometer, it is often necessary to estimate the temperature roughly. Despite the fact that the Galileo thermometer is not the most accurate instrument for measuring temperature, its working principle is still ingenious, making it a very peculiar decorative item.