Keith GriswoldMarch 13, 2000 Physical Chem.Dr. HumphreyHeat-Capacity Ratios for GasesMaterials of different types will exhibit varied changes in temperature when transferred the same amount of heat. This variation is a result of the difference in properties displayed from one material to another, known as “heat capacity.” Every substance has a variable, positive valued heat capacity that represents the amount of heat required to initiate a specific temperature change. (Hechinger, page 1) For ideal gases, there are heat capacities at constant volume and constant pressure given by:Cp = Cv + R The ratio, Cp = Cvis related to the ability of the gas to do expansion work. Heat capacity at constant volume, Cv can be described using the equipartition theory, which states that each mode of motion will contribute to a molecule or atom’s energy.E = E(translational) + E(rotational) + E(vibrational)Setting up a Cartesian coordinate system, translational motion can occur in any of the three directions: x, y, or z. Thus for a monatomic gas energy can be represented as 3(RT/2); it is clear that no vibrational or rotational motions contribute. Rotational motion contributes to the energy of diatomic and polyatomic molecules; they are easily accessible at room temperature therefore will significantly contribute to . Vibrations can be separated into two categories: bending and stretching, where the number of modes can be described as 3N-5 for linear, and 3N-6 for nonlinear molecules. Vibrational levels are not as accessible as rotational ones are at room temperature, so it is valid to consider them, at most, only partially active; the extent depends on certain properties of the molecule. Stretching modes tend to have very high frequencies giving way to a small contribution to heat capacity ratios. It should be noted that electronic transitions will be ignored since most molecules are in their elect...
