Heat Capacity Ratios for Gases

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Heat Capacity Ratios for Gases

Materials 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 = 

Cv

is 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 w...

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...al motions, (theoretical) would increase slightly to a value of 1.2500. It would be difficult to decipher between these two structures based off experimental values of , especially with such a questionable experimental setup. It is necessary to realize that the discrepancy between the two ratios, posed by the difference in structure, is small; such precision would be difficult to achieve.

Bibliography:

Brucat, P.J. Adiabatic Expansion: Cooling of Gases. CHM4411L; Physical Chemistry

Laborator, Fall 1996. http://itl.chem.ufl.edu/4411L_f96/gamma/gamma,html

Hechinger, Brandon. Lab4- The Ratio of Heat Capacities. Course: Physics 2; March 31,

1997. http://www.voyager.com/~jaggy/physics/lab4/.

McQuarrie, Donald A. Physical Chemistry; A Molecular Approach. University Science

Books; Sausalito, CA: 1997. Pages 169.

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