Problem $3$:

An air$-$conditioning system is shown in the figure, in which air flows over tubes carryig Refrigerant $134$a$.$ Air enters with a volumetric flow rate of $50\frac{m^3}{m}in$ at $32C,\frac{1}{b}ar$ and exits at $22C,\frac{0\mathrm{.}95}{b}ar.$ Refrigerant enters the tubes at $5$ bar with a quality of $20\%$ and exits at $\frac{5}{b}ar,20C.$ Ignoring heat transfer to the surroundings of the air$-$conditioning system, and neglecting the kinetic and potential energy effects, determine the following a steady state:

a$)$ The mass flow rate of the refrigerant, in $k\frac{g}{m}in$

b$)$ The rate of heat transfer, in $k\frac{J}{m}in,$ between the air and the refrigerant.

Assume air behaves as an ideal gas during the operation of the air$-$conditioning system.