= Solution
A source much deeper than the annual penetration depth has $T_S\simeq288.15$ K. Therefore
$$
\boxed{\mathrm{COP}_{\rm ground}=\frac{293.15}{5}=58.63,\quad
\frac{W_{\rm ground}}{W_{\rm direct}}=\frac5{293.15}=0.0171.}
$$
The ideal coldest-day electrical-input ratios are \b[direct : air-source : deep-ground = 1 : 0.0853 : 0.0171]. The deep source needs one fifth of the ideal air-source <work>. These ratios compare equal useful heating, and do not include excavation, circulation losses or an assumed real compressor efficiency.
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