= Entropy generated by cooling a finite body in a reservoir
{title2=$\Delta S_{\mathrm{tot}}=C[\ln(T_0/T_i)+T_i/T_0-1]$}
For a body of constant <heat capacity> $C$ cooling from $T_i$ to a <thermal reservoir> at $T_0>0$, the body's <entropy> change is $C\ln(T_0/T_i)$, while the reservoir gains $C(T_i-T_0)/T_0$. Their sum is nonnegative because $r-1-\ln r\geq0$ for $r=T_i/T_0>0$. The logarithmic body contribution is computed along a hypothetical reversible path; the actual finite-temperature-difference heat transfer is irreversible.
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