HC lab formal - Adam Romman Abstract Predictions made by...

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Adam Romman Abstract Predictions made by the equipartition principle and how well they matched experimental data were examined. Heat capacities were predicted based on number and type of degrees of freedom in 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 where involving vibrational degrees of freedom. The higher the vibrational contribution, the more the predictions deviated from experimental values. 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. 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. Vibrational : These refer to movements of atoms in the molecule about their equilibrium positions. 3N minus the translational and rotational degrees of freedom equal the number of vibrational degrees of freedom. Consequently, an atom, linear molecule, and nonlinear molecule will have 0, 3N-5, and 3N-6 vibrational degrees of freedom, respectively.
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According to the equipartition principle, each degree of freedom provides an energetic contribution toward the molecule’s C v , where C v is heat capacity at constant volume. The contribution from each translation and rotational degree of freedom is (RT)/2 while that from each vibrational degree of freedom is RT, where R is the ideal gas constant and T is the temperature. The following equation relates C v and internal energy, U.
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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.

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HC lab formal - Adam Romman Abstract Predictions made by...

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