Two $\mathrm{kg}$ of a gas is compressed in a process. Pressure $(P)$ and mass specific volume $(v)$ of the gas during the process follows: $P v^{1.2}=$ constant. The temperature of the gas before and after compression is $300$ $\mathrm{K}$ and $600$ $\mathrm{K}$, respectively. Assume that the gas behaves as an ideal gas with gas constant and ratio of specific heat capacities equal to $287 \mathrm{~J} / \mathrm{kg}-\mathrm{K}$ and $1.4$, respectively. The heat rejected (in $\mathrm{kJ}$) during the process is $\_\_\_\_$ (rounded off to two decimal places).
