Problem $4(10$ points$)-$ Second law analysis of an adiabatic heat exchanger

Ambient air at is to be preheated steadily by using hot exhaust combustion gases in a crossflow heat exchanger before it enters the furnace. Air enters the heat exchanger at $200$ kPa and $\backslash (20^\{\backslash$circ$\}\backslash$mathrm$\{$C$\}\backslash )$ at a volume flow rate of $\backslash (1\mathrm{.}5\backslash$mathrm$\{$~m$\}^\{3\}/\backslash$mathrm$\{$s$\}\backslash )$ and leaves at $180$ kPa $.$ The combustion gases enter at $\backslash (180\{\}^\{\backslash$circ$\}\backslash$mathrm$\{$C$\}\backslash )$ and $150$ kPa at a rate of $\backslash (2\mathrm{.}0\backslash$mathrm$\{$~kg$\}/\backslash$mathrm$\{$s$\}\backslash )$ and leave at $\backslash (95^\{\backslash$circ$\}\backslash$mathrm$\{$C$\}\backslash )$ and $140$ kPa $.$ Using the method of variable specific heats for your computations and assuming that the properties of combustion gases can be modeled as air in an adiabatic heat exchanger, please answer the following.

a$.$ Compute the outlet temperature of the air when it has been preheated, in $\backslash (\{\}^\{\backslash$circ$\}\backslash$mathrm$\{$C$\}\backslash ).$

b$.$ Determine the rate of heat transfer to the air that will be preheated.

c$.$ Compute the net rate of entropy transfer into the control volume by mass flow for each stream in the heat exchanger. Which stream has a decrease in net rate of entropy transfer by mass and which one an increase? See Equation $8-36$ in your textbook for the definition of the net rate of entropy transfer by mass into the control volume.

d$.$ For the process in the heat exchanger, compute the rate of entropy generation. Based on your numerical result, is the operation of the heat exchanger as described, feasible? Explain your reasoning.