problem $4(7$ points$)30$ mins

A vortex tube is a steady$-$state device that splits a high$-$pressure gas stream into two streams, one warm and one cool. During a controlled test, it was determined that $85\%$ of the compressed air entering the vortex tube went to the warm air stream and $15\%$ went to the cool air stream. Compressed air enters the vortex tube at $19\mathrm{.}3C,0\mathrm{.}52$MPa and a mass flow rate of $1\mathrm{.}5k\frac{g}{s}.$ Warm air leaves the vortex tube at $26\mathrm{.}3$@$C$ while the cool air leaves at $-21\mathrm{.}8$@$C.$ Both exit streams are at atmospheric pressure of $101\mathrm{.}35$ kPa $.$ The temperature of the surroundings can be assumed to be $20C.$

Determine: a$)$ the rate of heat loss from the vortex tube to the surroundings, $[kW]b)$ the rate of entropy generation in the vortex tube, $k\frac{W}{K}$

Note: Air can be modeled as an ideal gas with constant $Cp$ and $K$

Solution: