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Derive expressions for the rotational contribution to the molar internal energy
Accepted Answer
The rotational contribution to the molar internal energy (U_rot) can be derived using statistical mechanics and the equipartition theorem. For a linear molecule, the rotational energy is given by:
U_rot = (1/2)RT
where:
R is the ideal gas constant (8.314 J/mol
K)
T is the temperature in Kelvin
For a non-linear molecule, the rotational energy is given by:
U_rot = (3/2)RT
These expressions assume that the molecule is behaving as a rigid rotor. In reality, molecules have vibrational degrees of freedom, which also contribute to the internal energy. However, at low temperatures, the rotational contribution dominates.
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