= Solution
Using $c=2700\,\mathrm{m\,s^{-1}}$ gives the <electron-acoustic recoil length>
$$
\lambda=\frac{\hbar}{2m_ec}=2.1438\times10^{-8}\,\mathrm m.
$$
The <temperature> ratio therefore fixes
$$
\boxed{a=\frac{(6\pi^2)^{1/3}\lambda}{240}=3.482\times10^{-10}\,\mathrm m=0.3482\,\mathrm{nm}.}
$$
It follows that $n=4/a^3=9.48\times10^{28}\,\mathrm{m^{-3}}$, $k_F=1.4105\times10^{10}\,\mathrm{m^{-1}}$ and $k_D=1.7771\times10^{10}\,\mathrm{m^{-1}}$. Substitution gives
$$
\boxed{\theta_D\simeq366.5\,\mathrm K,\qquad T_F\simeq8.796\times10^4\,\mathrm K.}
$$
The resulting <Fermi energy> is about $7.58\,\mathrm{eV}$ and the <temperature> ratio is indeed $240$. These values follow from the supplied effective sound speed and free-electron/Debye approximations; they are not independent precision measurements of copper's parameters.
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