Improved Gay-Lussac Experiment Considering Added Volumes Available to Purchase

Gay-Lussac’s law states that the pressure of an ideal gas is directly proportional to its absolute temperature if the volume is constant. Students observe this relationship by taking measurements on the pressure of gas in a flask or metal sphere at different temperatures and then extrapolate the data to estimate absolute zero. In our college physics classes, we noticed that student estimates were always near −280 °C (vs. the correct value of −273.15 °C) when using a 125-ml flask or −315 °C with a 25-ml flask. In fact, instructor’s notes from Vernier and Carolina Supply provide estimates of −283 °C and −289 °C for absolute zero, respectively. Additional work has shown that the primary problem with the Gay-Lussac experiment is that the volume in the measurement system outside the heated flask or sphere must be minimized to get estimates of absolute zero close to the theoretical value. Increasing the flask or sphere size can minimize the error in this experiment. While these observations have been noted, these researchers did not present the full theory to explain this effect, or how to account for the volume outside the heated flask. Here we derive the theory for two connected volumes at two different temperatures and show why many experiments provide estimates of absolute zero that are too low. We also provide two alternative ways to estimate absolute zero using the two-volume model. These methods provide significant reduction in error and provide an excellent learning experience for students in introductory physics or chemistry classes.