Refrigeration Cycles

Refrigeration cycles transfer heat from a low-temperature reservoir to a higher-temperature reservoir by input of work. The most common practical cycle is the vapor-compression refrigeration cycle, consisting of (1) evaporator (heat absorption at low temperature), (2) compressor (work input, raising pressure and temperature), (3) condenser (heat rejection at high temperature, condensation), and (4) expansion device (pressure reduction, typically near-isenthalpic). Idealized bounds are given by the reversed Carnot cycle, which defines the maximum possible coefficient of performance (COP) between two absolute temperatures. Real cycles are characterized by irreversibilities (compressor inefficiency, pressure drops, non-ideal expansion) and enhancements (subcooling, superheating, multi-stage compression) that affect COP, refrigeration capacity, and power input.

Governing FormulaKey relations (SI units): - COP (refrigeration) = Q_L / W_net (dimensionless), where Q_L is heat absorbed at evaporator (W) and W_net is net work input (W). - Reversed Carnot COP: COP_Carnot = T_L / (T_H - T_L), with T_L and T_H in kelvin. - Refrigeration capacity (cooling rate): Q_dot_L = m_dot * q_L = m_dot * (h_1 - h_4) (W), with h in kJ/kg and m_dot in kg/s (convert kJ/s to kW). - Compressor work rate (steady flow): W_dot_comp = m_dot * (h_2 - h_1). - Expansion (throttle) for ideal valve: h_4 = h_3 (isenthalpic). - Isentropic compressor efficiency: eta_is = (h_2s - h_1) / (h_2 - h_1), where h_2s is enthalpy after isentropic compression to discharge pressure. - Practical assumptions: steady-state, negligible potential and kinetic energy changes, single-component refrigerant streams; for numerical problems, enthalpies are provided when needed to avoid reliance on property tables.

Knowledge Check

10 Questions

1.What is the correct definition of the coefficient of performance (COP) for a refrigeration system?

2.A reversed Carnot refrigerator operates between an evaporator at 5 °C and a condenser at 35 °C. What is the Carnot COP? (Use absolute temperatures in kelvin.)

3.For a vapor-compression cycle operating between fixed evaporator and condenser pressures, what is the main effect of subcooling the liquid refrigerant leaving the condenser (i.e., lowering its temperature below the saturation temperature)?

4.Which property remains (approximately) constant across a well-designed throttle (expansion) valve in a vapor-compression refrigeration cycle?

5.Which expression correctly defines the isentropic efficiency (eta_is) of a compressor in terms of specific enthalpies?

6.Consider a single-stage vapor-compression refrigeration cycle. Given the following steady-state per-unit-mass enthalpies: h_1 (evaporator outlet, saturated vapor) = 420 kJ/kg, h_2 (compressor outlet) = 480 kJ/kg, h_3 (condenser outlet, saturated liquid) = 120 kJ/kg. The expansion is isenthalpic so h_4 = h_3. The refrigerant mass flow rate is 0.05 kg/s. Calculate the refrigeration capacity (Q_dot_L) and the COP of the cycle.

7.If the condenser pressure (and thus condenser temperature) is increased while the evaporator pressure is held constant, what is the typical effect on the COP of a vapor-compression refrigeration system (other factors fixed)?

8.Which statement best describes the effect of using two-stage compression with intercooling (or flash intercooling) compared with single-stage compression for large pressure ratios in refrigeration?

9.A refrigeration compressor inlet state has h_1 = 420 kJ/kg; the isentropic discharge enthalpy at compressor outlet would be h_2s = 480 kJ/kg. If the compressor isentropic efficiency is 80% and the refrigerant mass flow is 0.10 kg/s, what is the actual compressor power input (W_dot_comp) in kW? (Use eta_is = (h_2s - h_1)/(h_2 - h_1).)

10.Which of the following is a correct general statement about the Carnot refrigeration cycle compared with real vapor-compression cycles operating between the same two temperature reservoirs?