Introduction, Background, Abstract
The heat capacity for a gas is specific for that particular gas and the conditions it is under. The heat capacity is defined as the amount of heat necessary to increase the temperature by one degree Celsius of one unit mass of a substance. Gamma (γ) is the ratio of the heat capacity at constant pressure and constant volume, respectively. The purpose of this laboratory was to determine the value of gamma (γ) for air, helium, argon, nitrogen and carbon dioxide. By observing gases during adiabatic compression the ratio of heat capacities at constant pressure and constant volume (γ) can be obtained.
To determine gamma (γ) for each substance being tested the pressure and volume of the gas must be monitored and recorded during a process of adiabatic compression. From the recorded data, the natural log of the pressure can be plotted against the natural log of the volume overtime for each run. The slope of this graph is equal to the gamma value for that gas. Gamma (γ) is equal to the slope of this graph because the following equation can be derived: (full derivation on subpage)
To hypothesize, it is likely that each gas that is tested will be determined to have a gamma (γ) value that is similar to its reported value in literature. The value of gamma can be theoretically determined because the equipartition theorem explains that each degree of freedom in a substance contributes R/2 to the specific heat capacity at constant volume. A mono-atomic gas has three translational degrees of freedom and therefore values of Cv=3/2R, Cp=5/2R and γ=5/3. A linear arrangement of gas molecules has three translational degrees of freedom and two axes of rotation resulting in values of Cv=5/2R, Cp=7/2R and γ=7/5. The γ for air, carbon dioxide, and nitrogen is known to be 7/5 because these gases all fall under the category of linear. Helium’s γ on the other hand is known to be 5/3 because it is a mono-atomic or point like gas. It is also possible that each gas will slightly deviate from the reported values because of vibrational properties the gas may have.