This project uses the Rüchardt experiment to determine the ratio of specific heats and hence the number of degrees of freedom f of different gases by measuring the frequency of damped simple harmonic motion where the gas provides the Hooke's law like spring of a cylinder–piston system. This project links mechanics, electromagnetism, thermodynamics, statistical mechanics and quantum mechanics making it an excellent synoptic experiment for a year 2 undergraduate student and we detail our implementation of this team-based learning project. We present, for the Rüchardt experiment, simple derivations of the main relationships that govern the experiment, a detailed data analysis of the physics of the apparatus and the experimental data. We find f(He) = 3.48 ± 0.14, f(N2) = 4.92 ± 0.24, f(Air) = 4.96 ± 0.25, f(CO2) = 6.46 ± 0.39 at room temperature and atmospheric pressure. The results for CO2 requires a statistical analysis of its vibrational modes. These results show that the expected results can be measured using fairly simple apparatus, coupled with careful analysis of large data sets.