Answer
$\dot{Q}=484\ kW$
$T_{1,out}=99.2°C$
Work Step by Step
Energy balance for the hot side:
$\dot{Q}=-\dot{m}_2c_{p_2}(T_{2,out}-T_{2,in})$
Given $\dot{m}_2=2\ kg/s,\ c_{p_2}=2.2\ kJ/kg.K,\ T_{2,out}=40°C,\ T_{2,in}=150°C$:
$\dot{Q}=484\ kW$
Energy balance for the cold side:
$\dot{Q}=\dot{m}_1c_{p_1}(T_{1,out}-T_{1,in})$
Given $\dot{m}_1=1.5\ kg/s,\ c_{p_1}=4.18\ kJ/kg.K,\ T_{1,in}=22°C$:
$T_{1,out}=99.2°C$