a$.)$ Calculate and plot the air specific impulse $I_{sp}$ and specific fuel consumption $SFC-=\frac{m_f^{}g}{T}$ as a function of the stagnation pressure ratio ${}_c$ for an ideal turbojet engine. Assume the flight Mach number to be $2\mathrm{.}7,$ with $=1\mathrm{.}4,T_0=400R,Q_R=19,000Bt\frac{u}{l}bm,c_p=0\mathrm{.}24Bt\frac{u}{l}bmR,$ and ${}_{}=6\mathrm{.}8.$ Plot the results over the range from ${}_c=1\mathrm{.}0$ to the point at which the thrust goes to zero. For this part, feel free to write a short spreadsheet program, or you can write a short computer program using the language of your choice. If you do so$,$ please attach the spreadsheet $($and program, if you developed one$).$

b$.)$ Obtain an analytic expression for the compressor ratio, ${}_{cm},$ that just leads to zero thrust. Write ${}_{cm}$ in terms of $,M_0,$ and ${}_{}.$ Check that the value calculated using the data of part $($a$)$ agrees with the graphical result of part $($a$).$