Q$7.$

$[15$ marks$]$

Heat in the amount of $150kJ$ is transferred directly from a hot reservoir at $T_H{?}_{?}=550K$ to two cooler reservoirs at $T_1=350K$ and $T_2=250K.$ The surrounding temperature is $T_0=300K.$ If the heat transferred to the reservoir at $T_1$ is half that transferred at $T_2,$ calculate:

$($a$)$ The entropy generation in $kJ{K}^{-1}$

$($b$)$ The lost work.