Power, Refrigeration Cycles, Psychrometrics, and Second Law

Name the cycle before calculating

Power and refrigeration questions are pattern-recognition problems before they are formula problems. A Rankine cycle uses pump, boiler, turbine, and condenser. A Brayton cycle uses compressor, combustor or heat addition, turbine, and heat rejection. Otto and Diesel cycles are air-standard models for reciprocating engines, distinguished mainly by constant-volume versus constant-pressure heat addition. A vapor-compression refrigeration cycle uses compressor, condenser, expansion valve, and evaporator.

Once the cycle is named, label the states around it. The FE Reference Handbook formulas assume a state order. If you swap compressor outlet with condenser outlet, the arithmetic may look clean but the heat and work terms will be assigned to the wrong component.

Efficiency versus COP

A heat engine produces net work from heat input, so thermal efficiency is W_net,out / Q_in. It must be less than one. A refrigerator consumes work to move heat from a cold space, so COP_R = Q_L / W_in. A heat pump's useful effect is heat delivered to the warm space, so COP_HP = Q_H / W_in. For the same device, COP_HP = COP_R + 1 when energy balances are idealized.

Do not reject a refrigerator COP above one. COP is not efficiency. It compares moved heat with work input, and it can exceed one because the device is moving heat rather than converting all input directly into work.

Second-law limits

The second law sets direction and limits. A cyclic heat engine cannot convert all heat input into net work while rejecting no heat. Heat does not naturally flow from cold to hot without work input. Entropy generation is nonnegative for real processes. Reversible models are ideal limits, not ordinary machine performance.

Carnot formulas use absolute temperatures. Heat-engine Carnot efficiency is 1 - T_C/T_H. Refrigerator and heat-pump Carnot COP formulas also use absolute reservoir temperatures. Using Celsius is a classic FE trap because ratios and differences become physically wrong.

Isentropic efficiency compares real adiabatic devices with ideal isentropic devices. For a turbine, real work output is less than ideal work output. For a compressor or pump, real work input is greater than ideal work input. This means the efficiency formula is arranged differently for turbines and compressors. Write what is useful divided by what is required for that device instead of memorizing a single fraction blindly.

Property-table cycles

Rankine and vapor-compression cycles often require table lookup. In a simple Rankine cycle, turbine inlet may be superheated steam, condenser outlet may be saturated liquid, pump work may be approximated with v Delta p, and boiler heat input is an enthalpy rise. In vapor compression, the expansion valve is modeled as throttling, so enthalpy is approximately constant across it. Compressor work is based on enthalpy rise, and refrigeration effect is evaporator enthalpy rise.

Psychrometrics

Psychrometrics treats moist air as dry air plus water vapor. The usual chart variables are dry-bulb temperature, wet-bulb temperature, relative humidity, humidity ratio, dew-point temperature, specific volume, and moist-air enthalpy. Heating air without adding moisture raises dry-bulb temperature and lowers relative humidity while humidity ratio stays about constant. Cooling below the dew point removes moisture, so humidity ratio decreases. Evaporative cooling adds water vapor and usually lowers dry-bulb temperature while increasing humidity ratio.

FE psychrometric questions are often qualitative or one-chart-step quantitative. Always identify the process line first: sensible heating, sensible cooling, cooling with dehumidification, humidification, or mixing.