A four-components gas mixture comprising of 44.7 kPa methane (CH4), 57 kPa ethane (C2He), 60.3 kPa propane (CaHs), and 39.7 kPa n-butane (CaH10) flows in a brass pipe. By considering a pipe section as the control volume, it is found that the iniet and outlet temperatures are 107C and 138C. For the pipe section, an electric-powered (7motor = 76.4%) fan (voltage = 240 V, ampere = 10.5 A) and an electrical (nmotor = 100%) heater (resistance = 22.15 0, ampere = 12.5 A) are installed to ensure good mixing and provide heating, separately. On a summer day, the non-adiabatic pipe that installed outside the production plant is gaining heat from ambient at a rate of 26 kW. As the pipe section is uniform and has no sharp edge, there is no pressure drop as the fluid flows through it. Given respective molar mass of CH4, C2H6, C3H8, and CaH10 is 16.04 g/mol, 30.07 g/mol, 44.1 g/mol, and 58.12 g/mol. Take R, as 8.314 kJ/kmol-K. W, Electrical heater Wsh Control volume Fan Electrical motor (a) Determine the total pressure of the system, the mole fraction of each gas species, and the molar mass of the gas mixture. (4 Marks) (b) Calculate the change of specific enthalpy of the gas mixture. (6 Marks) Table C.1: Heat Capacities of Gases in the Ideal-Gas State* Constants in equation p/Ru =A + BT + CT? + DT-2 for T (K) from 298 K to Tmax Chemical species Tmax pzoa/Ru A 10' B 106 C 10-sD CH4 9.081 -2.164 -5.561 -8.824 Methane 1500 1500 4.217 6.369 9.011 1.702 1.131 1.213 ...... 19.225 28.785 Ethane ..... Propane n-Butane C,Hs CH10 1500 1500 11.928 1.935 36.915 -11.402 (c) Calculate the electrical power of electrical heater and the shaft power of the fan. (4 Marks) (d) Determine the mass flow rate of the gas mixture in this pipe section.