Past exam of the physics B course of the University of Cambridge / 2018 / Paper 2 / Section A / A2 / Solution

Use absolute temperatures $T_c=278.15\mathrm{K}$ and $T_h=298.15\mathrm{K}$. Let ${\dot{Q}}_c$ be the heat extracted from the ground, ${\dot{Q}}_h$ the heat delivered indoors, and $P$ the electrical input power. For a reversible heat pump, the entropy transferred per unit time balances:Consequently the coefficient of performance isThe requested heat delivery is a rate, since the duration is unspecified:Of this, $13.9\mathrm{kW}$ comes from the ground and $1.0\mathrm{kW}$ from the electricity. A coefficient of performance greater than one is consistent with conservation of energy because the heat pump transports heat as well as converting electrical energy.