anudoneddbv

2022-07-15

A superconducting ring can carry a current for an indeﬁ nite length of time. Isn’t this a perpetual motion machine, which violates the ﬁ rst or second law of thermodynamics? Explain.

Tamoni5e

Expert

Perpetual motion machine is a kind of machine which can do work without any energy input.
A Superconductor is an hypothetical material which offers zero resistance. The entropy change in a superconducting material is zero as it is a highly ordered material.
From Second law of thermodynamics:
$\mathrm{△}S=\frac{\mathrm{△}Q}{T}\phantom{\rule{0ex}{0ex}}0=\frac{\mathrm{△}Q}{T}\phantom{\rule{0ex}{0ex}}\mathrm{△}Q=0$
From first law of thermodynamics:
$\mathrm{△}Q=\mathrm{△}U+\mathrm{△}W\phantom{\rule{0ex}{0ex}}0=\mathrm{△}U+\mathrm{△}W\phantom{\rule{0ex}{0ex}}\mathrm{△}W=-\mathrm{△}U$
Since internal energy of a superconductor is constant.
$\mathrm{△}U=0$
Then,
Work done, $\mathrm{△}W=0$
But, in this case the superconductor is carrying the current for indefinite amount of time so work done can't be zero. So it is violating the First Law of Thermodynamics.

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