= Entropy generation in finite-temperature heat transfer
{title2=$dS_{\rm tot}=dQ(1/T-1/T_R)$}
When a system at instantaneous <temperature> $T$ absorbs <heat> $dQ$ from a reservoir at $T_R$, with no other <entropy> production in the system, its <entropy> increases by $dQ/T$ while the reservoir changes by $-dQ/T_R$. The total is positive for spontaneous <heat> transfer across a finite <temperature> difference. A quasistatic mechanical path can therefore be thermally irreversible.
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