$1\mathrm{.}1$ Revisit. Rework Problem $1\mathrm{.}1,$ but now using a thermodynamic analysis assuming complete combustion.

Determine the vacuum specific impulse $I_{sp,\text{v}\text{a}\text{c}}$ of an oxygen$-$hydrogen rocket engine with an oxidizer$-$tofuel mixture ratio by weight of $4\mathrm{.}0$:$1.$ Calculate adiabatic flame temperature assuming complete combustion with a chamber pressure of $68$atm through a convergent$-$divergent nozzle expanded to vacuum. Report the product flame temperature and molecular weight. Calculate the specific impulse. Compare your values to those from Problem $1\mathrm{.}1.$ Discuss and assess your results with consideration of the chemical composition of the exhaust products.

Assume hydrogen and oxygen at $298\mathrm{.}15$K$.$ Assume adiabatic and isentropic flow through the nozzle with an expansion area ratio $=50$:$1.$

Note, you will need thermodynamic enthalpy tables for $H2,O2$ and $H2O$ as a function of temperature.