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jaejoon89
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How do you use the equipartition theorem to calculate molar specific heat for hydrogen gas?
Can somebody please explain how it works?
Can somebody please explain how it works?
kingkool said:There are 3 degrees of translational freedom, 2 of rotational freedom, 1 degree of vibrational freedom. The vibrational freedom is not accessible at room temperature, at higher temperatures it is but let's stick with room temperature.
So that's 5 degrees of freedom per molecule. So if you have a lot of molecules (N number of molecules), there are 5N degrees of freedom. each contributes 1/2kT to internal energy (U), for a total of 5/2kt*N..
So U = 5/2kT*N
dU/dT = heat capacity = 5/2K*N = 5/2R (for 1 mole, k*N_avagadro = R)
The molar specific heat of a gas can be calculated using the equipartition theorem, which states that each degree of freedom of a molecule contributes a certain amount of energy to the total heat capacity. For hydrogen gas, which has three degrees of freedom (translational, rotational, and vibrational), the molar specific heat can be calculated as C = (3/2)R, where R is the gas constant (8.314 J/mol·K).
The molar specific heat of a gas is a measure of how much heat energy is needed to raise the temperature of one mole of the gas by one degree. For hydrogen gas, the molar specific heat is important in understanding its thermal properties and behavior, as well as in various industrial and scientific applications.
No, the molar specific heat of hydrogen gas is not constant at all temperatures. According to the equipartition theorem, the molar specific heat of a gas increases with temperature, since higher temperatures allow for greater energy contributions from the molecule's degrees of freedom. Therefore, the molar specific heat of hydrogen gas will vary at different temperatures.
The molar specific heat of hydrogen gas is relatively low compared to other gases, such as oxygen and nitrogen, which have five degrees of freedom and molar specific heats of (5/2)R. This is due to the fact that hydrogen gas has fewer degrees of freedom and therefore less energy is required to raise its temperature.
Yes, the equipartition theorem can be used to calculate the molar specific heat of any gas that follows the ideal gas law, as long as the number of degrees of freedom is known. However, for more complex molecules with additional degrees of freedom, the calculation may become more complicated and may require additional thermodynamic principles.