Problem $4-$ Energy Balance $(10$ pts$)$

Two kilograms of refrigerant $22,$ initially at $p_1=0\mathrm{.}9$MPa,$u_1=232\mathrm{.}92k\frac{J}{k}g,$ is contained within

a rigid, closed, and well$-$insulated tank. The tank is fitted with a paddle wheel that transfers

energy to the refrigerant at a rate of $K*t,$ in kW $,$ where K is a constant in kW per minute, and t

is time in minutes. After $10$ minutes of stirring, the refrigerant is at $p_2=1\mathrm{.}2$MPa and $u_2=$

$276\mathrm{.}67k\frac{J}{k}g.$ No overall changes in kinetic and potential energy occur. $($a$)$ For the refrigerant,

determine the heat transfer and the work through the process, each in kJ$.($b$)$ Determine the

value of the constant K appearing in the given relation, in $k\frac{W}{m}in.$