= Solution
At fixed $N$ and $b$, the <entropic spring> constant is proportional to absolute <temperature>, because the <free energy>[free-energy] penalty for a given loss of <conformational entropy> is $-T\Delta S$. Therefore
$$
\boxed{k(10^\circ\mathrm C)=k(25^\circ\mathrm C)\frac{283.15}{298.15}=0.94969\,k(25^\circ\mathrm C).}
$$
For the literal printed chain this is $\boxed{1.287\times10^{-6}\,\mathrm{N\,m^{-1}}}$. The same factor multiplies either alternative contour-consistent <spring constant> from part (d), provided its <Kuhn length> is held fixed. Real <DNA>'s <persistence length>, <base pairing> and solvent interactions can themselves vary with <temperature> and salt; then $b(T)$ contributes through $k\propto T/b(T)^2$ at fixed segment count, or $k\propto T/[L_cb(T)]$ if the physical contour is instead held fixed. The simple linear <temperature> result belongs to the specified ideal-chain model.
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