Answer
$\dot{Q}=29.26\ kW$
$T_{2,out}=117.4°C$
Work Step by Step
From the energy balance on the cold side:
$\dot{Q}+\dot{m}_1h_{1,in}=\dot{m}_1h_{1,out}$
With $h_{1,out}=h_{1,in}+c_{p_1}(T_{1,out}-T_{1,in}),\ c_{p_1}=4.18\ kJ/kg.K$,
$\ \ \ \ T_{1,out}=60°C,\ T_{1,in}=25°C,\ \dot{m}_1=0.2\ kg/s$:
$\dot{Q}=29.26\ kW$
For the hot side:
$\dot{Q}=\dot{m}_2c_{p_2}(T_{2,out}-T_{2,in})$
Given $T_{2,in}=140°C,\ c_{p_2}=4.31\ kJ/kg.K,\ \dot{m}_2=0.3\ kg/s$
$T_{2,out}=117.4°C$
