Agas undergoes a process from state $1,$ where $p_1=415$kPa,$v_1=0\mathrm{.}37\frac{m^3}{k}g,$ to state $2,$ where $p_2=138$kPa, according to $p{v}^{13}=$ constant. The relationship between pressure, specific volume, and specific internal energy is

$u=1\mathrm{.}443pv-221\mathrm{.}557$

where $p$ is in kPa,$v$ is in $\frac{m^3}{k}g,$ and $u$ is in $k\frac{J}{k}g.$ The mass of gas is $4\mathrm{.}5$ kg $.$ Neglecting kinetic and potential energy effects, determine the heat transfer, in kJ$.$