Problem $4(21$ points$)$

A jet propulsion system is being designed for operation on Mars, which has an atmosphere that can be approximated as $C{O}_2.$ Rather than a combustion process to heat working fluid, an external source $($e$.$g$.,$ nuclear reaction$)$ will be used. Martian atmosphere enters the propulsion system at a mass flow rate of $5k\frac{g}{s}.$ The system layout and properties at key points are given in the figure below.

Note: You may assume that all components other than the heater operate adiabatically and that kinetic energy is negligible except at the diffuser inlet and nozzle outlet.

Note: Among the complexities of operating in the Mars atmosphere that are not explored in this problem, the density of ambient $C{O}_2$ is $\frac{1}{100}$ of ambient air on Earth, which will reduce aerodynamic lift over the wings of the aircraft equipped with this propulsion system by the same factor.

a$)$ What is the temperature, in K $,$ at the diffuser exit? $(6$ points$)$

b$)$ If the turbine exists solely to provide mechanical work to drive the compressor, what is the enthalpy at its exit, in $k\frac{J}{k}g?(6$ points$)$

c$)$ What is the nozzle exit velocity, in $\frac{m}{s}?(5$ points$)$

d$)$ How much thrust, in kN $,$ is produced by the propulsion system? $(4$ points$)$