A Galileo thermometer named after Italian physicist Galileo Galilei

Galileo Galilei

Galileo Galilei , was an Italian physicist, mathematician, astronomer, and philosopher who played a major role in the Scientific Revolution. His achievements include improvements to the telescope and consequent astronomical observations and support for Copernicanism...

, is a thermometer

Thermometer

Developed during the 16th and 17th centuries, a thermometer is a device that measures temperature or temperature gradient using a variety of different principles. A thermometer has two important elements: the temperature sensor Developed during the 16th and 17th centuries, a thermometer (from the...

 made of a sealed glass

Glass

Glass is an amorphous solid material. Glasses are typically brittle and optically transparent.The most familiar type of glass, used for centuries in windows and drinking vessels, is soda-lime glass, composed of about 75% silica plus Na2O, CaO, and several minor additives...

 cylinder

Cylinder (geometry)

A cylinder is one of the most basic curvilinear geometric shapes, the surface formed by the points at a fixed distance from a given line segment, the axis of the cylinder. The solid enclosed by this surface and by two planes perpendicular to the axis is also called a cylinder...

 containing a clear liquid

Liquid

Liquid is one of the three classical states of matter . Like a gas, a liquid is able to flow and take the shape of a container. Some liquids resist compression, while others can be compressed. Unlike a gas, a liquid does not disperse to fill every space of a container, and maintains a fairly...

 and a series of objects whose densities are such that they rise or fall as the temperature changes. By definition, Galileo's thermometer is actually a thermoscope, not a thermometer.

Normal design

Suspended in the cocoare a number of weights. Commonly those weights are themselves attached to sealed glass bulbs containing colored liquid for aesthetic effect. As the liquid in the cylinder changes temperature

Temperature

Temperature is a physical property of matter that quantitatively expresses the common notions of hot and cold. Objects of low temperature are cold, while various degrees of higher temperatures are referred to as warm or hot...

, its density

Density

The mass density or density of a material is defined as its mass per unit volume. The symbol most often used for density is ρ . In some cases , density is also defined as its weight per unit volume; although, this quantity is more properly called specific weight...

 changes and the bulbs are free to move – rising or falling to reach a position where their density is either equal to that of the surrounding liquid or where they are brought to a halt by other bulbs. If the bulbs differ in density by a very small amount and are ordered such that the least dense is at the top and densest at the bottom, they can form a temperature scale.
The temperature is typically read from an engraved metal disc on each bulb. Usually a gap separates the top bulbs from the bottom bulbs and then the temperature would be between the tag readings on either side of the gap. If a bulb is free-floating in the gap, then its tag reading would be closest to the ambient temperature.

To achieve satisfactory accuracy, the weights are required to be manufactured to a tolerance of less than 1/1000 of one gram (1 milligram (3.5273962105112E-05 oz)).

Theory of operation

The Galilean thermometer works due to the principle of buoyancy

Buoyancy

In physics, buoyancy is a force exerted by a fluid that opposes an object's weight. In a column of fluid, pressure increases with depth as a result of the weight of the overlying fluid. Thus a column of fluid, or an object submerged in the fluid, experiences greater pressure at the bottom of the...

. Buoyancy determines whether objects float or sink in a liquid, and is responsible for the fact that even boats made of steel

Steel

Steel is an alloy that consists mostly of iron and has a carbon content between 0.2% and 2.1% by weight, depending on the grade. Carbon is the most common alloying material for iron, but various other alloying elements are used, such as manganese, chromium, vanadium, and tungsten...

 can float (while a solid bar of steel by itself will sink).

The only factor that determines whether a large object will rise or fall in a particular liquid relates the object's density to the density of the liquid in which it is placed. If the object's mass is greater than the mass of liquid displaced, the object will sink. If the object's mass is less than the mass of liquid displaced, the object will float.
Suppose there are two objects, each a cube 10 by 10 by 10 cm (3.9 by 3.9 by 3.9 in) (i.e., 1 l (2.1 US pt)). The mass of water displaced by an object of this size is 1 kg (2.2 lb). The brown object on the left is floating because the mass of water it would displace if completely submerged (1 kg (2.2 lb)) is greater than the mass of the object. It floats half submerged because that is the point where the mass of the water displaced (0.5 kg (1.1 lb)) is equal to the mass of the object. The green object on the right has sunk because the mass of water it is displacing (1 kg (2.2 lb)) is less than the object's mass (2 kg (4.4 lb)).

Not all objects made of the green material above will sink. In Figure 2, the interior of the green object has been hollowed out. The total mass of the object is now 0.5 kg (1.1 lb), yet its volume remains the same, so it floats half way out of the water like the brown object in Figure 1.

In the examples above, the liquid in which the objects have been floating is assumed to be water. Water has a density of 1 kg/L, which means that the mass of water displaced by any of the above objects when fully submerged, is 1 kg (2.2 lb).

Galileo discovered that the density of a liquid is a function of its temperature. This is the key to how the Galileo thermometer works; as the temperature of water increases from 4 °C (39.2 °F), its density decreases.

Figure 3 shows a 1 kg (2.2 lb) hollow object made of the green material. In the left hand container, the density of the liquid is 1.001 kg/L. Since the object weighs less than the water it displaces, it floats. In the right hand container, the density of the liquid is 0.999 kg/L. Since the object weighs more than the mass of the water it displaces, it sinks. This shows that very small changes in the density of the liquid can easily cause an almost-floating object to sink.

In the Galileo thermometer, the small glass bulbs are partly filled with a different (coloured) liquid. Once the handblown

Glassblowing

Glassblowing is a glassforming technique that involves inflating molten glass into a bubble, or parison, with the aid of a blowpipe, or blow tube...

 bulbs have been sealed, their effective densities are adjusted by means of the metal tags hanging from beneath them. The expansion due to the temperature change of the coloured liquid and air gap (called ullage

Ullage

Ullage or Headspace refers to the unfilled space in a container, particularly with a liquid.-Etymology:The word comes ultimately from the Latin oculus, “eye”, which was used in a figurative sense by the Romans for the bung hole of a barrel...

) inside the bulbs would affect their density were it not for the almost fixed volume of the glass bulb. The clear liquid in which the bulbs are submerged is not water, but some inert hydrocarbon

Hydrocarbon

In organic chemistry, a hydrocarbon is an organic compound consisting entirely of hydrogen and carbon. Hydrocarbons from which one hydrogen atom has been removed are functional groups, called hydrocarbyls....

whose density varies with temperature more than water's density does. This change of density of the clear liquid, with temperature change, causes the bulbs to rise or sink.

Figure 4 shows a schematic representation of a Galileo thermometer at two different temperatures (the temperature markings on this example are in Fahrenheit).

If there are some bulbs at the top (Figure 4, left) and some at the bottom, but one floating in the gap, then the one floating in the gap (green 76 °F (24.4 °C)) tells the temperature. If there is no bulb in the gap (Figure 4, right) then the average of the values of the bulb above and below the gap gives the approximate temperature.
The bulbs and weights should be sized so as not to jam with each other, either by being at least half the size of the tube diameter to retain their stacking order or, as an alternative, much less than the tube diameter to freely pass each other in the tubes.