Quality Grade (Second Law Efficiency)

Also referred to as second-law efficiency or exergetic efficiency.

The quality grade of a heat pump describes the ratio between the actual Coefficient of Performance (COP) a heat pump achieves in practice and the theoretical maximum possible Carnot COP. It shows how closely a machine can approach the thermodynamic optimum, and reflects the real-world energy losses within the refrigeration cycle. The quality grade can be calculated using the following formula:

Formula: Quality grade = COP_actual / COP_Carnot

A quick reminder: the Carnot cycle is an idealized process that can never actually be achieved by real equipment. Using the formula below, the actual COP can be calculated from the quality grade and the Carnot COP — the latter derived from the absolute temperatures (in Kelvin) of the source temperature at the evaporator (T_E) and the heat output temperature at the condenser (T_C).

Formula: COP_actual = T_C / (T_C − T_E) × quality grade

Worked example (brine/water heat pump, new build vs. existing building)

New building, B0/W35:

• Evaporator temperature: T_E = 273.15 K + 0 °C = 273.15 K
• Condenser temperature: T_C = 273.15 K + 35 °C = 308.15 K
• COP_Carnot = 308.15 K / (308.15 K − 273.15 K) ≈ 8.8
• Assumed quality grade: 50%
• COP_actual = 8.8 × 0.50 ≈ 4.4

Existing building, B0/W55:

• Evaporator temperature: T_E = 273.15 K + 0 °C = 273.15 K
• Condenser temperature: T_C = 273.15 K + 55 °C = 328.15 K
• COP_Carnot = 328.15 K / (328.15 K − 273.15 K) ≈ 6.0
• Assumed quality grade: 50%
• COP_actual = 6.0 × 0.50 ≈ 3.0

This example illustrates why the actual COP in an existing building with radiators (55 °C flow temperature) comes out at around 3 — noticeably lower than the 4.4 achieved with underfloor heating (35 °C flow temperature): the larger temperature lift between the source and the flow temperature reduces the Carnot COP, and with it, the achievable actual COP.

Typical quality grade values range from 40–65%: roughly 40–50% for basic units, 50–60% for standard/mid-range units, and 60–65% for excellent units. The quality grade is the only metric that allows the device quality of different heat pumps to be compared independently of their respective temperature lift.