  The finite temperature Casimir free energy, entropy, and internal energy are
considered anew for a conventional parallel-plate configuration, in the light
of current discussions in the literature. In the case of an "ideal" metal,
characterized by a refractive index equal to infinity for all frequencies, we
recover, via a somewhat unconventional method, conventional results for the
temperature dependence, meaning that the zero-frequency transverse electric
mode contributes the same as the transverse magnetic mode. For a real metal,
however, approximately obeying the Drude dispersive model at low frequencies,
we find that the zero-frequency transverse electric mode does not contribute at
all. This would appear to lead to an observable temperature dependence and a
violation of the third law of thermodynamics. It had been suggested that the
source of the difficulty was the behaviour of the reflection coefficient for
perpendicular polarization but we show that this is not the case. By
introducing a simplified model for the Casimir interaction, consisting of two
harmonic oscillators interacting via a third one, we illustrate the behavior of
the transverse electric field. Numerical results are presented based on the
refractive index for gold. A linear temperature correction to the Casimir force
between parallel plates is indeed found which should be observable in
room-temperature experiments, but this does not entail any thermodynamic
inconsistency.

Quantum Physics;High Energy Physics - Theory