Chapter 5 - Mass and Energy Analysis of Control Volumes - Problems - Page 272: 5-191

$T_3=\dfrac{\dot{m}_1}{\dot{m}_3}T_1+\dfrac{\dot{m}_2}{\dot{m}_3}T_2$

$\dot{m}_1+\dot{m}_2=\dot{m}_3$ $\dot{m}_1h_1+\dot{m}_2h_2=\dot{m}_3h_3$ $\dot{m}_1c_pT_1+\dot{m}_2c_pT_2=\dot{m}_3c_pT_3$ $T_3=\dfrac{\dot{m}_1}{\dot{m}_3}T_1+\dfrac{\dot{m}_2}{\dot{m}_3}T_2$