You are tasked to help design a hydrazine thruster for a satellite. The thruster should be able to produce 350mN of thrust (at steady state) with a total impulse of 410kNs. The thruster is intended to operate with a hydrazine storage tank regulated to 25atm and held at a constant storage temperature of 290K. A high pressure (maximum of 65atm ) nitrogen tank and regulator will be used to maintain the hydrazine tank at the prescribed operating pressure. The line pressure loss between the hydrazine tank and the exit of the catalyst bed is estimated to be 0.3atm. The catalyst engineer has informed you to expect the products leaving the catalyst bed to consist only of NH3,N2, H2, with NH3 making up 30% of the mixture (by mole). For this preliminary design exercise, assume the thruster will use a bell nozzle having an area ratio of 20 and a length that is 70% of the length of a conical nozzle with 15 half-angle having the same exit area as the bell nozzle (hint: you can use the data of Fig. 3-14 in Sutton, or the following figure). Use the following data for the gas properties. Here, universal gas constant R:8.314J/molK (a) What is the mole fraction of the NH3 produced by the N2H4 decomposition? Start with this reaction: N2H4n3NH3+n6H2+ncN2 and set up the atom balance equations for N and H. (b) Using the thermodynamic properties from the table above (and from nowhere else) and assuming all gases are ideal (calorically perfect), determine the temperature (T), averaged molecular weight (MW), averaged specific heat (cp) and averaged specific heat ratio () of the products exiting the catalyst bed. Assume an adiabatic chamber, no work and steady state. (c) Based on your results from part (b), find the exit velocity, exit temperature, and specific impulse of the thruster assuming frozen chemistry in the nozzle. (d) Determine the required throat diameter (Dt) and total length (LN) of the thruster nozzle