Atmospheric Pressure Measurement Using a Smartphone

We believe that laboratory work deepens students' understanding and makes meteorology theory more directly relevant to the real world. In meteorology, the hydrostatic equation relates the pressure difference between two altitudes to the weight of the air column between those altitudes, which is determined by air density, gravitational acceleration, and the change in altitude. Therefore, we can compute the pressure difference based on the air density (1.293 g/m³ at STP), gravitational acceleration, and the known altitude difference.

We incorporate laboratory activities using an iPhone, as modern smartphones have various applications that can indicate altitude and atmospheric pressure. Since our laboratory is located in a five-story building with a fire exit staircase and an open-air atrium, students are asked to measure the atmospheric pressure and altitude on each floor of both locations.

First, the students plot the measured altitude versus the corresponding atmospheric pressures. The results should show a linear relationship between altitudes and pressures for all data. This is because a smartphone's application computes the altitude based on the measured pressure value, assuming a constant temperature.

As we know the actual altitude of each floor in our building from the building's blueprints, students are asked to plot the known altitude of each floor versus the measured pressures. This time, they will find a linear relationship for both the fire exit staircase and the open-air atrium, but they will notice differences in the slopes of the linear regression lines for each location. The difference in slope is due to the temperature difference, as inferred from the hydrostatic equation and ideal gas law. As an extension, students may take data in the morning and afternoon and then compare the results to observe any potential temperature effects.

Using the air density at STP and the known altitude difference, students can compute the expected pressure difference and then compare it with the measured value. The measured pressure difference should be smaller than the computed value. Asking why the measured value was smaller than expected will provide a good opportunity to confirm the students' understanding of the meaning of STP and the inverse relationship between air density and temperature.

While pressure sensors in smartphones can accurately measure pressure differences, they cannot obtain absolute pressure values. Based on our experience, the accuracy of pressure difference measurements is generally quite good, but some phones may show strange results. Therefore, it is recommended that students work in groups, compare their data within the group, and collaborate on writing a report.

Our experiment was initially designed for in-person laboratory activities in regular classes. However, the experiment can also be adapted for students working remotely in an online course setting. The designed activity can be implemented in a high-rise apartment building and/or a large shopping mall.