= Solution
\b[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):
$$
\frac{d\overline T_C}{dP}=\frac1{2W_Cc_C},
\quad
\frac{d\overline T_M}{dP}=R_2+\frac1{2W_Cc_C},
\quad
\frac{d\overline T_F}{dP}=R_1+R_2+\frac1{2W_Cc_C}.
$$
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>
$$
\boxed{
\alpha_P
=\alpha_FR_1+(\alpha_F+\alpha_M)R_2
+\frac{\alpha_F+\alpha_M+\alpha_C}{2W_Cc_C}.
}
$$
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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