Past exam of the MPhil in micro- and nanotechnology enterprise course of the University of Cambridge / 2022 / Paper 1 / Section B / 12 / iii / b / Solution

Use absolute temperatures $T_H=523.15\mathrm{K}$, $T_C=323.15\mathrm{K}$ and $\overline{T}=423.15\mathrm{K}$. With the explicit identical-per-leg interpretation from the preceding part,and the stated ideal efficiency expression givesWith the alternative already-combined pair convention, $Z\overline{T}=0.6488$ instead gives ${\eta }_{\max }\simeq 5.71\%$. Both lie below the Carnot efficiency $1-T_C/T_H=38.2\%$. These are constant-property ideal conversion efficiencies, neglecting contact resistance, parasitic heat paths and temperature dependence. They are not the efficiency specifically at the maximum-power load.