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Question I (25 pts). Streams of ethane and air (79 mole\% N2, the balance O2) are combined at the inlet of a combustion furnace preheater. The pressures of each stream are measured with open-end mercury manometers, the temperatures are measured with resistance thermometers, and the volumetric flow rates are measured with orifice meters. The flowmeter of the ethane stream reads 912m3/h and the flowmeter of the air stream reads 186m3/min. Pressure readings at the mensurement points 1,2 and 3 are 221mm,145mm and 79mm, respectively. Renistance thermometers measure the resistances at the measurement points 1. 2 and 3 as 25.342 ohms, 25.321 ohms and 42.642 ohms, respectively. Atmospheric pressure is measured with a sealed end mercury manometer as 29.57 in. The resistance thermometers were calibrated by measuring their resistances at the freezing and boiling points of water, with the following results: T=0C,r=23.352 olms T=100C,r=31.977ohms A straight-line relationship between T and r may be assumed. The relationship between the total molar flow rate of a gas and its volumetric flow rate is, to a good approximation, given by a form of the ideal gas equation of state: (skmol)T(K)12.186P(atm)V^(m3/s) where P is the absolute pressure of the gas. a) Derive the resistance thermometer calibration formula for T(C) in terms of r (ohm). b) Convert the given gas law expressions to an expression for n(kmol/min) in terms of P ( mmHg),T(C), and V(m3/min). c) Calculate the temperatures (in K ) and pressures (in mmHg ) at measurement points 1.2, and 3 . d) Calculate the molar flow rate of the combined gas stream in kmol/min. e) Calculate the reading of flowmeter at measurement point 3 in m3/min. f) Calculate the total mass flow rate (kg/min) and the mass fraction of the ethane at measurement point 3