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A low annual electricity indicator does not by itself reveal how closely a heat-pump installation approaches the thermodynamic limit of its heating task. This paper develops a second-law screening model anchored to the documented 35/28 °C heating design temperatures of an anonymised nonresidential building. The source is a baseline-only consultancy report, not an operational monitoring dataset. A finite water-temperature change is represented using an entropy-based effective temperature. Reversible work, a task-level reversible coefficient of performance and the exergy efficiency of hypothetical operating points are evaluated across outdoor-source temperatures of −10, 0 and 10 °C. Higher supply/return pairs of 45/38 and 55/48 °C are introduced as explicit comparison scenarios. At a source temperature of 0 °C, the 35/28 °C task has a reversible coefficient of performance of approximately 9.68. Assuming a second-law efficiency of 0.45 gives a scenario COP of 4.35; raising the water temperatures to 55/48 °C increases electricity per unit heat by approximately 53.45% under that same-efficiency assumption. Conversely, fixing COP at 3 produces different second-law efficiencies across temperature tasks, showing why COP alone is an incomplete comparison metric. The analysis uses heat delivered as a normalisation basis and does not convert the scenarios into annual building savings. Its contribution is a reproducible thermodynamic map and an explicit measurement boundary for subsequent commissioning assessment. The actual seasonal efficiency, refrigerant-cycle irreversibilities and domestic-hot-water performance remain unverified.
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Süleyman Tiryaki (2026) studied this question.
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