formal2 - Adam Romman Heat Capacity Ratio of Gases Abstract...

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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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2. 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 non-linear molecules have three degrees of rotation since they can rotate about all three axes. 3.
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This note was uploaded on 09/07/2009 for the course CH N/a taught by Professor Genemcdonald during the Spring '09 term at University of Texas at Austin.

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formal2 - Adam Romman Heat Capacity Ratio of Gases Abstract...

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