Not just melting ice: a simple experiment demonstrates how thermal expansion contributes to rising sea levels as one of the consequences of climate change.
The planetary ocean is a mass of water that covers most of our planet and interconnects all parts of the globe. It plays an important role in the Earth's climate and, although a complex system, still obeys the simple laws of physics and chemistry taught in schools. When teaching these laws, teachers can use this example to raise awareness of the dynamics of the ocean and its impact on our lives.
When talking about a rise in sea level due to global heating, many people think only of melting ice sheets and glaciers and do not realise that thermal expansion is actually a significant factor.
Most materials expand when heated. We say 'most materials' because water in the liquid state does not follow this trend between 0 and 4°C. Despite this behaviour, above 4°C, water will expand when heated. This is one of the problems with an increase in the sea-surface temperature – the water dilates and contributes to rising sea levels. Thermal expansion is responsible for about 43% of rising sea levels, which pose a serious threat to populations living along coastlines.
Students can see first-hand how water behaves with temperature. This simple experiment is suitable for students aged 11–14 and demonstrates how the volume of water changes with temperature. The activity lasts about 15 minutes.
Older students can expand on Activity 1 to roughly calculate the thermal expansion coefficient of water. This physical quantity, in K-1, can be calculated using the following equation:
where ΔV is the variation (increase) in volume, V is the initial volume, and ΔT is the variation in temperature.
This is a rough calculation because, as proposed, the experiment contains several errors that are difficult to overcome, as we will explain below. However, if this is acknowledged and the main objective is not to determine an exact value for the coefficient of thermal expansion, but rather a value of the same order of magnitude as the actual one, students can still perform measurements and draw some conclusions.
One of the problems with this experiment is that the thermal expansion coefficient of water varies with temperature: for example, at 10°C it is 8.8×10-5 K-1, at 20°C it is 2.07×10-4 K-1, and at 30°C it is 3.03×10-4 K-1. The value is also small; therefore, to allow a measurable variation in water volume, it is best to use a significant initial volume of water and a significant variation in temperature.
The activity is suitable for students aged 14–16 and lasts about 45 minutes.
In this experiment, we obtained the following values:
|Ti [°C]||Ti [K]||Tf [°C]||Tf [K]||ΔT [K]||ΔV [cm3]||V [cm3]|
Using equation (1), water's coefficient of thermal expansion can be calculated:
Ask the students for possible sources of error.
As explained previously, the value is not exact and will probably be higher than the actual value for the range of temperature applied in the experiment, but it is still of the same order of magnitude.
How can this value be translated into a rise in sea level? After all, the coefficient is very small, the water affected by the rise in temperature of the ocean is mainly that closer to the surface, and even this increase is small compared to the temperature change in the experiment. However, students should not be deceived by this; the ocean is massive, and even a small increase in temperature will cause an expansion of the ocean that contributes to rising sea levels.
Although the ocean does not have a homogeneous temperature, on average, a 700 m deep section of ocean has increased in temperature by 0.1°C from 1961 to 2003. With some simplifications, it is possible to estimate the rise in sea level for the situation described.
Present the following problem to your students: let us assume that the ocean is a column with area A and height h, or volume V = A×h. How much will the water level rise, or the height of a 700 m column of water change, if water heats up by 0.1°C (0.1 K) and it can only expand vertically (in the direction of the height of the column)? Tell the students to assume that the value of αV they calculate is an acceptable approximation.
Using equation (1), students can do the following calculation:
As mentioned, this is a simplification. Thermal expansion is not linear with temperature, and the ocean also expands inland, with the rise in water level depending on the gradient of the coast. Nevertheless, the result highlights the point that this expansion is not negligible.
So, even a small increase in temperature of 0.1°C can translate into a significant rise in sea level. And this is only thermal expansion at play; the rise in temperature of the planet also causes melting of the ice sheets and glaciers, which contributes to the rise in sea levels. On average, and over the last 25 years, the sea level has been rising by about 3 mm a year, as determined from satellite data, and this rise is accelerating.
Questions to ask the students:
 ESA infographics on the causes of rising sea levels: https://www.esa.int/ESA_Multimedia/Images/2018/09/Causes_of_sea-level_rise
 An online calculator to determine volumetric temperature expansion: https://www.engineeringtoolbox.com/volumetric-temperature-expansion-d_315.html
 Silver J (2008) Global Warming and Climate Change Demystified. McGraw-Hill. ISBN: 0-07150-240-8
 A video from ESA on rising sea levels: https://www.esa.int/ESA_Multimedia/Videos/2018/09/Sea-level_rise/
 Satellite data on sea levels: https://climate.nasa.gov/vital-signs/sea-level/