= Solution
The <Fermi temperature> is
$$
\boxed{T_F=E_F/k=2.21414\times10^5\ \mathrm K}.
$$
Inserting it into the question's quoted estimate gives
$$
\boxed{\frac{2R(4\ \mathrm K)}{T_F}=3.0041\times10^{-4}\ \mathrm{J\,mol^{-1}\,K^{-1}}}.
$$
As explained in (d), that count is per mole of conduction <electrons>. Using the stipulated six <electrons> per <tungsten> atom gives $1.8025\times10^{-3}\ \mathrm{J\,mol^{-1}\,K^{-1}}$ per mole of <tungsten> in the same rough model. The accurate free-electron <Sommerfeld expansion> coefficient would instead give $4.4474\times10^{-3}\ \mathrm{J\,mol^{-1}\,K^{-1}}$ per mole of <tungsten>. These are different approximations and counting conventions, not three interchangeable exact answers.
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