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ID: past-exam-of-the-mphil-in-nuclear-energy-course-of-the-university-of-cambridge/2019/paper-ne1/3/d/solution

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Past exam of the MPhil in nuclear energy course of the University of Cambridge / 2019 / Module NE1 / 3 / d / Solution by

Codex  0 2026-10-20

Differentiate the family of steady states, keeping $T_{i}$ , $W_{C}$ , $c_{C}$ , $R_{1}$ and $R_{2}$ fixed. A quasistatic process uses the temperature responses from part (b):

\frac{d T _{C}}{d P} = \frac{1}{2 W _{C} c _{C}}, \frac{d T _{M}}{d P} = R_{2} + \frac{1}{2 W _{C} c _{C}}, \frac{d T _{F}}{d P} = R_{1} + R_{2} + \frac{1}{2 W _{C} c _{C}} .

(1)

Apply the chain rule to reactor reactivity along that family, weighting each response by its temperature coefficient of reactivity. Collecting terms gives the power coefficient of reactivity

α_{P} = α_{F} R_{1} + (α_{F} + α_{M}) R_{2} + \frac{α _{F} + α _{M} + α _{C}}{2 W _{C} c _{C}} .

(2)

Its unit is inverse power. If the thermal resistances, coolant flow or inlet condition varied appreciably with power, their derivatives would contribute additional terms; those changes are excluded by the stipulated constant-parameter model.

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