$($Show work and circle$/$box final answers$)$ Problem $6$

The device shown in the figure below can take two airstreams and produce a single exhaust stream.

At inlet $1,$ the mass flow rate is $5k\frac{g}{s},$ the temperature is $288$ K $,$ and the pressure is $0\mathrm{.}101$ MPa $.$ At

inlet $2,$ the mass flow rate is a fraction $$ of the mass flow rate of inlet $1,$ the temperature is $1500$ K $,$

and the pressure is $5$ MPa $.$ The ratio of specific heats of the working fluid is $=1\mathrm{.}4,$ and the specific

heat at constant pressure is constant. Mass, momentum, and energy exchange mechanisms occur

inside the device. Assuming the device operates in a steady state and the kinetic and potential

energies at all stations are insignificant, determine the maximum pressure at outlet $3$ in the following

two cases:

a$)$ Case $1$: in terms of alpha $()$

b$)$ Case $2$: if $m_2^{}$ is $0\mathrm{.}5k\frac{g}{s}$