Compressor Work (Isentropic)
Compute the specific compression work in an ideal refrigeration cycle, W = h₂ − h₁, the enthalpy difference between the compressor outlet and inlet (isentropic compression, at constant entropy). It is the energy the compressor adds to the refrigerant per kilogram — the cycle's 'electricity bill'. Together with the refrigerating effect, it defines the COP (COP = refrigerating effect/work). Enter the outlet and inlet enthalpies.
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Compressor work (isentropic)
In the vapor-compression refrigeration cycle, the compressor is the heart — and the only component that consumes energy (the system's 'electricity bill'). Ideally the compression is isentropic (constant entropy, with no losses and no heat exchange), and the specific work is simply the enthalpy difference: W = h₂ − h₁ (kJ/kg). That is the energy step the refrigerant vapor takes on as it gets compressed from the low evaporator pressure to the high condenser pressure. Compressor work is half the COP story: COP = refrigerating effect / compressor work. An efficient cycle maximizes the heat absorbed in the evaporator (the refrigerating effect) and minimizes the work spent — hence the value of never compressing more than needed (moderate pressure ratios) and of keeping temperature differences small. Real compressors have isentropic efficiencies of 70–85%, consuming more than the ideal figure. On the pressure-enthalpy (P-h) diagram, the work is the horizontal span of the compression line. Enter the enthalpies at the compressor outlet and inlet.
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Carnot COP (Refrigeration)
Compute the maximum theoretical coefficient of performance (COP) of a refrigerator, COP = Tc/(Th − Tc), with temperatures in kelvin, where Tc is the cold-source (evaporator) temperature and Th the hot-source (condenser). It is the limit set by the 2nd law of thermodynamics: no real refrigerator can exceed it. The smaller the temperature difference between the sources, the higher the possible COP — which is why refrigerating to very low temperatures is so costly. Enter the cold and hot temperatures in kelvin.
Back Work Ratio (BWR)
Calculate the back work ratio (BWR) of a power cycle, BWR = w_compressor ÷ w_turbine, dividing the work consumed by the compressor (or pump) by the gross work produced by the turbine. The dimensionless result shows what fraction of turbine work is reinvested to compress the fluid. In gas turbines (Brayton cycle) the BWR is high (0.4–0.6), since compressing gas is costly; in steam Rankine cycles it is tiny (~0.01), since pumping liquid is cheap. A high BWR makes the cycle sensitive to component efficiencies. Enter the compressor work and the turbine work.
Superheat Degree
Compute the superheat of a refrigeration system, ΔT = T_suction − T_evaporation(saturation), how much hotter the refrigerant vapor is than its saturation temperature at the evaporator pressure. Proper superheat (typically 5–10 °C) ensures only vapor (no liquid) reaches the compressor, protecting it from liquid slugging. Too much superheat reduces capacity. It is controlled by the expansion valve. Enter the suction and saturated evaporation temperatures.
Boost Converter (Step-Up)
Calculate the output voltage of a boost (step-up) DC-DC converter in continuous conduction, V_out = V_in ÷ (1 − D), from the input voltage V_in and the duty cycle D (0 to 1). The result, in volts, is always greater than the input — the boost converter raises voltage by storing energy in an inductor and releasing it in series with the source. As D approaches 1, the output tends to infinity (limited by real losses). It is used in supplies that must step up voltage (LEDs, batteries, power factor correction) and in photovoltaic systems. Enter the input voltage and the duty cycle.
Compressor Volumetric Displacement
Compute the volumetric displacement of a reciprocating compressor, Vd = (π/4)·D²·L·n, the volume swept by the pistons, from the cylinder bore (D), the stroke (L) and the number of cylinders (n). It is the compressor's 'displacement' — the theoretical volume aspirated per revolution, which, multiplied by the speed and the volumetric efficiency, gives the actual flow. It defines the compressor capacity. Enter the bore, the stroke and the number of cylinders.
Rankine Cycle Efficiency
Calculate the thermal efficiency of a Rankine cycle, η = (w_turbine − w_pump) ÷ q_boiler × 100%, dividing the net work (turbine work minus pump work) by the heat added in the boiler, all in kJ/kg. The Rankine cycle is the basis of steam power plants: water is pumped, heated and vaporized in the boiler, expands through the turbine producing work, then condenses. The result, in %, measures how much boiler heat becomes useful work; real cycles run 30–45%. Enter the turbine work, the pump work and the boiler heat.
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