LECTURE PHYSICAL CHEMISTRY 3rd EDITION ROBERT G. MORTIMER

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4.3. Additional Useful Thermodynamic Identities
We have asserted without proof that (∂U/∂V) T ,n
vanishes for an ideal gas. We can now prove this
assertion and can obtain a formula that allows
evaluation of this derivative for nonideal gases and
liquids. We convert Eq. (4.2-3) to a derivative
equation by nonrigorously “dividing” by dV,converting
the quotients to partial derivatives, and specifying
that T and n are held fixed. The process is
mathematically indefensible, but gives the correct
derivative relation:
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