Adam Romman
Heat Capacity Ratio of Gases
Abstract
The theoretical prediction of heat capacities of argon, nitrogen, and carbon
dioxide made by the equipartition principle was compared to experimental data. Heat
capacities were predicted based on number and type of degrees of freedom in the three
different gases. The heat capacity of each gas was experimentally determined by first
recording the speed of sound in each gas and using the appropriate equations to get the
heat capacity. The speeds of sound in each gas were measured in two ways; the first
involved wavelength measurement, and the second involved frequency measurement.
The wavelength measurement method proved more accurate due to difficult in
instrumentation with the frequency measurement method. It was concluded that heat
capacity predictions made by the equipartition principle proved to closely mirror
experimental values, except in those cases involving vibrational degrees of freedom.
Experimental heat capacities in J/(K*mol) for helium, nitrogen, and carbon dioxide were
12.60, 20.86, and 29.35 respectively.
In the same order, theoretical heat capacities with
vibrational contributions were 12.47, 29.10, and 54.04, and without vibrational
contributions were 12.47, 20.77, and 38.38. Because helium, nitrogen, and carbon
dioxide have increasing numbers of vibrational degrees of freedom, it can be seen that
increasing vibrational contribution corresponds to greater deviation between predictions
from the equipartition principle and experimental values for heat capacity.
Introduction
The heat capacity of a substance relates the amount of heat absorbed to the
temperature change of a substance. The heat capacity of a substance is correlated to the
number of degrees of freedom the substance has. This relationship is known as the
equipartition principle. This experiment investigates how well an experimentally
determined heat capacity relates to the heat capacity predicted by the equipartition
principle. Experimentally determined heat capacities of various gases are found by
measuring the speed of sound in gas.
Theory
Degrees of freedom refer to the number of positional arrangements a molecule
may have. A molecule had 3N degrees of freedom, where N equals the number of atoms
in the molecule. Degrees of freedom can be classified into three categories
1
.
1.
Translational
: These refer to motion in the three dimensions. All molecules
have three translational degrees of motion.
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Rotational
: These refer to molecular rotation about an axis. Atoms have no
distinguishable rotational and so have zero degrees of freedom. Linear
molecules have two degrees of freedom because they can rotate about two
axes, while nonlinear molecules have three degrees of rotation since they can
rotate about all three axes.
3.
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 Spring '09
 GeneMcDonald
 Physical chemistry, pH

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