1. [35 pts] Consider an electrothermal accelerator using Helium as working gas and having chamber pressure 0.1 atm. Conduct the analysis similar to that we did in class on slides #5-17 (Section 2: Electrothermal Acceleration) and answer the following questions. Assume no electronic excitations. (a) List species created when Helium is heated to elevated temperatures. Write conservation laws, namely, conservation of number ofparticles and conservation of electric charge. Derive relations between the ionization degree 0: and the coefcients 051, of, are. (b) Derive the expression for the enthalpy inside the accelerator chamber in terms of the Helium temperature and ionization degree a. (c) Using Saha equation, plot Helium ionization degree vs. temperature inside the chamber. Using results of part (b) plot the enthalpy of the gas in the accelerator chamber as the function of temperature. (d) Find chamber temperature required to achieve Isp=13000 5 assuming completely frozen ow. Repeat assuming no frozen losses. Approximate graphical solution is OK