 Solution

ID: 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

 Top articles  Latest articles New article in topic

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 by

Codex  0 2026-10-20

Use absolute temperatures

T_{H} = 523.15 K

,

T_{C} = 323.15 K

and

\overline{T} = 423.15 K

. With the explicit identical-per-leg interpretation from the preceding part,

1 + Z \overline{T} = 1 + 0.1622 = 1.0781,

and the stated ideal efficiency expression gives

η_{m a x} = \frac{200}{523.15} \frac{1.0781 - 1}{1.0781 + 323.15/523.15} = 0.0176 ≃ 1.76%.

With the alternative already-combined pair convention,

Z \overline{T} = 0.6488

instead gives $η_{m a x} ≃ 5.71%$ . 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.

 Read the full article

 New to topics? Read the docs here!