ronic ground state at room temperature. Applying classic statistical mechanics to the equipartition theory, an expression for the energy contribution of one mole of a gas from each mode of motion is given as RT/2. Since heat capacity varies with temperature the following relationship is given:Cv = (E/T)v. (E is the internal energy)Using these relationships, a theoretical value of can be derived. In contrast, experimental values will be calculated through an adiabatic expansion method initiated by Clement and Desormes. Discrepancies between the experimental values and those predicted by the equipartition theory will be examined. Theoretical Calculations:Theoretical values for can be calculated using the equipartition theory and the relationship Cp = Cv + R. The gases of interest for this experiment are argon, nitrogen, and carbon dioxide. Argon is monatomic, therefore we will only be looking at it’s translational motions. Cv will equal 3R/2 and Cp will equal 5R/2, leaving with a value of 1.6667. Nitrogen is a linear diatomic molecule, therefore rotational modes must be accounted for; a value of will be calculated with and with out vibrational contribution. Cv for nitrogen without vibrational acknowledgement is equal to 5R/2 and Cp is equal to 7R/2, leaving equal to 1.4000. Taking vibrational contributions into account, Cv will equal 3R and will then be 1.3333. Carbon dioxide is triatomic, but is still linear so Cv is 5R/2 and Cp is 7R/2, letting equal 1.4000. With vibrational modes included, equals 1.2222. All of these values are summarized in a table below along with experimental ones.Experimental:The adiabatic expansion process will be carried out using the experimental setup illustrated below.Apparatus SchemeA gas of interest is placed in the carboy and pressure readings are then recorded. The carboy is closed off with a rubber sto...
