$2)$ Determine and plot the specific impulse of an ideal ramjet flying at an altitude of $10$ km $,$ that uses JP$-10$ as its fuel $($assume JP$-10$ is stored at $298$ K $)$ as a function of flight Mach number $(\backslash (2\backslash$leq $\backslash$mathrm$\{$M$\}\_\{0\}\backslash$leq $8\backslash ),$ intervals of $1$ are fine$).$ On the same plot, include the specific impulse for the same ramjet at the same conditions, but instead uses a fuel comprising $\backslash (70\backslash \%\backslash )$ by weight JP$-10,$ and $\backslash (30\backslash \%\backslash )$ by weight boron. In this initial part assume an equivalence ratio of $1.$

Provide an explanation for the trends.

Now plot the specific impulse of an ideal ramjet under the same conditions, but operating with an equivalence ratio of $0\mathrm{.}5($you can choose either fuel case from the first part, you don't have to do both$).$ Whichever fuel you select, please compare the corresponding performance from the first part of the problem where you can assume it operated at stoichiometric conditions. Again, please provide an explanation for the differences you observe. $(15$ points$)$