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Worked Examples · Example 4.1

Q.Calculate the internal energy of argon and oxygen.

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Monatomic argon has 3 translational degrees of freedom → U = (3/2)kT; diatomic oxygen adds 2 rotational → U = (5/2)kT.

Argon is a monatomic gas. The internal energy of an ideal gas depends only on its temperature, through the equipartition of energy — each degree of freedom carries ½kT. A monatomic atom has only 3 translational degrees of freedom, so

UAr=32kT per molecule.U_{\text{Ar}} = \tfrac{3}{2}kT \text{ per molecule.} …

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