Boiling Water at High Altitudes: A Representation of American Scientific Literacy

A recent survey by the Pew Research Center found that Americans are more likely to answer correctly questions related to basic science concepts than to scientific understanding [1]. Among the bank of questions, ones such as which layer of the earth is hottest and whether uranium is used in nuclear energy were answered correctly more often than ones such as whether the amplitude of sound waves causes its loudness. The question answered incorrectly most often was whether water at higher altitudes boils at lower temperatures with only 34% of respondents knowing that, indeed, it does.

Fig. 1: Results of Pew Research Center survey (Pew Research Center, same as reference 1)

Public scientific literacy is an important goal to work towards for developed countries. As Cary Funk and Sara Kehaulani Goo of the Pew Research Center posit, the ability to understand scientific concepts is crucial to people being well enough informed about current issues such as GMOs and the energy crisis to make educated decisions in the polls. Scientific literacy also makes daily life easier by finding more efficient solutions to everyday problems.

As a small step towards improving scientific understanding, let us discuss why it is easier to boil water at higher altitudes.

Liquid water and water vapor exist in a sort of equilibrium. There are a number of factors that can shift this equilibrium, but one we interact with daily is temperature. Say you spill a glass of water. Of course, a large spill would require immediate attention, but if only a thimbleful of water was spilt, some would be inclined to let it evaporate. Evaporation involves two main processes at play. First, the water is receiving kinetic energy from its surroundings in the form of heat energy. Second, the water is in higher concentration in the spill than in the spill’s surroundings and therefore a concentration gradient is formed at the water’s surface.

So what has this all got to do with boiling water? Well, water boils when transforming into a gas. Therefore, boiling water is a phase transition described by the equilibrium between liquid water and water vapor. Besides temperature, pressure also affect liquid-gas equilibrium as described by the ideal gas equation,

                  1.       PV=nRT (P is pressure, V is volume, n is number of molecules in moles, R is the gas
                   constant, T is temperature)

LeChatelier’s principle states that a system in equilibrium will move away from an induced change. In the case of an increase in pressure, we can see that if n and T remain the same then the ideal gas law describes a shift to decrease V, volume. On the other hand, a decrease in pressure should cause a shift towards a higher V. This means that at lower pressures, water prefers to exist in a gaseous state and the equilibrium shift will cause the water to boil. This is the foundational concept of rotary evaporators, which use the concept of reduced-pressure boiling to remove solvents.

Fig. 2: Deriving atmospheric pressure in atm's (Pearson)

Now all that is left is to link pressure to altitude, which isn’t too hard. By definition, atmospheric pressure is defined as the weight of the atmosphere over an area at sea level [2]. For example, one inch of land at sea level partitions a pillar of atmosphere weighing 14.7 lbs, so atmospheric pressure in PSI is 14.7 lbs/in². A logical extension of this concept would tell us that at any altitude greater than sea level, the pillar of air would be shorter and would consequently weigh less. This is the missing link we were searching for between pressure and altitude. Putting all of the above information together, we see that a decrease in pressure causes liquid water to favor boiling and that an increase in altitude causes atmospheric pressure to decrease. Therefore, water boils easier at higher altitudes.

Scaling the results of the survey to education levels, the Pew Research Center also found a correlation between higher education and scientific knowledge. But this is not a given. Even as college students, we must all work towards insuring that we are among the scientifically literate ready to contribute educated opinions to today's social debates.