 Solution

For $N$ identical couples connected electrically in series, the open-circuit voltage is $N\mathcal{E}$ and the internal resistance is $NR$. At the module's matched load $R_{L,\mathrm{module}}=NR$,Maintaining the stated temperature difference across every couple therefore requiresunder the identical-per-leg interpretation. Sixty-four ideal couples supply about $3.02\mathrm{W}$; sixty-three supply about $2.97\mathrm{W}$. The alternative already-combined pair-resistance convention gives 32 couples, each producing approximately $0.0944\mathrm{W}$.

The module is thermally parallel: adding couples increases the heat flow that must be supplied and rejected. The count assumes that source and sink keep the actual leg junctions at the stated temperatures and that interconnect losses are negligible. Connecting the couples does not multiply the maintained temperature difference.