$5-17$ Refrigerant$-134$a enters a $28-cm-$diameter pipe steadily at $200$ kPa and $20C$ with a velocity of $5\frac{m}{s}.$ The refrigerant gains heat as it flows and leaves the pipe at $180$ kPa and $40C.$ Determine $($ a$)$ the volume flow rate of the refrigerant at the inlet, $($b$)$ the mass flow rate of the refrigerant, and $($c$)$ the velocity and volume flow rate at the exit.

This is a complete work$-$out problem requiring the following: system,sketch,conditions,physical laws,properties, and calculations.