Answer
$\dot{Q}=67.93\ kW$
$T_{1,out}=120°C$
Work Step by Step
Energy balance for the hot side:
$\dot{Q}=-\dot{m}_2c_{p_2}(T_{2,out}-T_{2,in})$
Given $\dot{m}_2=0.95\ kg/s,\ c_{p_2}=1.1\ kJ/kg.K,\ T_{2,out}=95°C,\ T_{2,in}=160°C$
$\dot{Q}=67.93\ kW$
For an ideal gas:
$\dot{m}=\frac{P\dot{V}}{RT}$
With $P=95\ kPa,\ R=0.287\ kJ/kg.K,\ \dot{V}=0.6\ m³/s,\ T=293\ K$:
$\dot{m}=0.6778\ kg/s$
On the cold side:
$\dot{Q}=\dot{m}_1c_{p_1}(T_{1,out}-T_{1,in})$
$T_{1,out}=120°C$
