please also read the notes

Streams of methane and air (79mole%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. Data: Flowmeter 1: V1=947m3/h Flowmeter 2: V2=195m3/min Manometer 1: h1=232mm Manometer 2:h2=156mm Manometer 3: h3=74mm Resistance thermometer 1: r1=26.159 ohms Resistance thermometer 2:r2=26.157 ohms Resistance thermometer 3:r3=44.789 ohms Atmospheric pressure: A sealed-end mercury manometer reads h=29.76 in. The resistance thermometers were calibrated by measuring their resistances at the freezing and boiling points of water, with the following results: T=0C;T=100C:r=23.624ohmsr=33.028ohms 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: n(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 and pressures at points 1, 2, and 3. (d) Calculate the molar flow rate of the combined gas stream. (e) Calculate the reading of flowmeter 3 in m3/min. (f) Calculate the total mass flow rate and the mass fraction of the methane at point 3. - For part (fl, assume that the composition of air is 21 mole %02 and 79 mole % N2