Design thermal system 1 question -- 2

When a single refrigerant condenses and evaporates at a constant pressure between saturated liquid and saturated vapor, the temperature remains constant. A binary solution, on the other hand, experiences a change in temperature, as pointed in Chap. 5. When a refrigeration system cools a fluid stream through a large temperature as it passes through the condenser, it may be possible to conserve compression power by using a binary solution. Some applications of this concept have been made in the cryogenic and petrochemical industries. The refrigeration cycle adaptable to refrigerant mixtures employs the usual components (compressor, condenser, evaporator, and expansion device) and a heat exchanger as well, as shown in Fig. A-13. A mixture of refrigerants R-12 and R-114 will be explored. Data 5 kW/K evaporator UA= 5 kW/K condenser 0.3 kW/k heat exchanger The condenser is water-cooled; water enters at 25°C with a flow rate of 0.8 kg/s. The evaporator fluid is cooled from -15 to -25°C. Its flow rate is 0.57 kg/s, and its specific heat is 3.5 kJ/(kg.K). The refrigerant is saturated liquid at point 3 and saturated vapor at point 1. The compressor has adjustable capacity which is regulated to provide the specified refrigeration rate in the evaporator. For saturated pressure R-12 lnp= 14.861-2498.3/T R-114 lnp= 15.407-2993.2/T Where p = pressure, kPa T= temperature, K For enthalpy of saturated liquid 200 + 0.925t + 0.00081t2 R-12 hf = 200 + 0.9545t + 0.00116t2 R-114 Where hf = enthalpy of liquid, kJ/kg, t = temperature, °C For enthalpy of saturated vapor 351.5 + 0.4283t -0.00071t2 R-12 hg= 337.4 + 0.6234t – 0.000086t2 R-114 where hg = enthalpy of saturated vapor, kJ/kg t = temperature. °C Work of compression ∆h={█(188 (1-(14.861-ln⁡〖p_2 〗)/(14.861-ln⁡〖p_1 〗 )) R-12@ 158 (1-(15.407-ln⁡〖p_2 〗)/(15.407-ln⁡〖p_1 〗 )) R-114)┤ Where ∆h = work of compression, kJ/kg p2 = discharge pressure (total pressure), kPa p1 = suction pressure (total pressure), kPa When compressing a mixture, the work of compression is found by proportioning according to the mass fraction of the constituents in the mixture. The mixture is assumed to be ideal, and Dalton’s and Raoult’s laws apply. The molecular weights of R-12 and R-114 are 120.93 and 170.94, respectively. Because the pressure changes as the refrigerant flows through the pipeline, the density and velocity also change. Account for the pressure drop in all pipes if the length from the compressor to the throttling device is 10 m (one way). The pipe cost in dollars per meter length is 300 D1.6, where D is the pipe diameter in meters. Assignment For the specified refrigeration duty (approximately 20kW), determine the composition of the mixture that results in minimum power requirements at the compressor. Required in 5 day.......