Heat Pumps

A heat pump is a device that transfers thermal energy from a lower-temperature reservoir (source) to a higher-temperature reservoir (sink) by consuming work. In building heating applications the objective is to deliver heat to the indoor space (Q̇_h) using electrical or mechanical work (Ẇ) while extracting heat from the outside air, ground or water (Q̇_c). The most common practical heat pump is the vapor-compression cycle: evaporation at low pressure absorbs heat from the source, compression raises refrigerant pressure/temperature, condensation rejects heat to the sink, and expansion reduces pressure (approximately isenthalpic). Performance is measured by the coefficient of performance (COP), which for heat pumps is the ratio of heat delivered to work input. The thermodynamic upper bound is given by a reversible (Carnot) heat pump operating between the source and sink temperatures. Real performance is reduced by irreversibilities, nonideal components, pressure drops, and finite heat-transfer driving forces. Typical design goals are to maximize delivered heat per unit electrical input and to minimize temperature lift (sink minus source temperature).

Governing FormulaDefinitions and useful relations (SI units): - Energy balance: Q̇_h = Q̇_c + Ẇ (steady-state first law for the heat pump) - COP (heat pump): COP_hp = Q̇_h / Ẇ - COP (refrigerator): COP_ref = Q̇_c / Ẇ - Relation: COP_hp = COP_ref + 1 (since Q̇_h = Q̇_c + Ẇ) - Carnot (reversible) heat pump COP_hp,Carnot = T_h / (T_h - T_c) with T_h, T_c in kelvin (K) - Minimum reversible input work to deliver Q̇_h: Ẇ_min = Q̇_h * (1 - T_c / T_h) - For vapor-compression with mass flow ṁ and specific enthalpies h_i (kJ/kg): Ẇ_comp = ṁ (h_2 - h_1) Q̇_cond = ṁ (h_2 - h_3) Q̇_evap = ṁ (h_1 - h_4) ; expansion h_4 ≈ h_3 (isenthalpic throttling) - Practical notes: COP decreases with increasing temperature lift (T_h - T_c); COP can exceed unity because the heat delivered includes both extracted heat and input work.

Knowledge Check

10 Questions

1.Which expression correctly defines the coefficient of performance (COP) of a heat pump used for space heating?

2.A reversible (Carnot) heat pump operates between outdoor temperature 270 K and indoor temperature 295 K. What is the maximum theoretical COP for space heating?

3.A heat pump must supply 10.0 kW of heat to a house. Its measured seasonal COP is 3.5. What electrical power does the heat pump consume (approx)?

4.How are the COPs of a heat pump (for heating) and a refrigerator (for cooling) related when they operate between the same two reservoirs?

5.What is the minimum (reversible) electrical work required to deliver 5.00 kW of heat to the indoor space for a reversible heat pump operating between T_h = 293 K (indoor) and T_c = 273 K (outdoor)?

6.In a vapor-compression heat pump, which component is primarily responsible for raising the refrigerant pressure and temperature?

7.If the condenser (delivery) temperature of a heat pump is raised while the evaporator (source) temperature remains fixed, what is the general effect on COP assuming the same irreversibilities?

8.A vapor-compression heat pump has mass flow ṁ = 0.050 kg/s. Measured specific enthalpies are h1 (evaporator outlet, compressor inlet) = 420 kJ/kg, h2 (compressor outlet / condenser inlet) = 450 kJ/kg, and h3 (condenser outlet, liquid) = 180 kJ/kg. Assuming isenthalpic expansion (h4 = h3), what are the condenser heat output and the cycle COP (Q̇_h / Ẇ)?

9.Can the coefficient of performance (COP) of a heat pump exceed unity (COP > 1)?

10.For a heat pump operating between fixed outdoor temperature T_c and an indoor setpoint T_h, what is the effect on COP if the thermostat is raised (T_h increases) while T_c stays constant?