Answer:[tex]T_3=55.21^{\circ}[/tex]
Explanation:
Given
mass of stream 1 is [tex]\dot{m_1}=30 kg/s[/tex]
Temperature [tex]T_1=90^{\circ}C[/tex]
mass of stream [tex]\dot{m_2}=200 kg/s[/tex]
Temperature [tex]T_2=50^{\circ}C[/tex]
mass of third stream [tex]\dot{m_3}[/tex]
[tex]\dot{m_1}+\dot{m_2}=\dot{m_3}[/tex]
[tex]30+200=\dot{m_3}[/tex]
[tex]\dot{m_3}=230 kg/s[/tex]
Balancing Energy
[tex]\dot{m_1}h_1+\dot{m_2}h_2=\dot{m_3}h_3[/tex]
[tex]\dot{m_1}T_1+\dot{m_2}T_2=\dot{m_3}T_3[/tex]
[tex]30\cdot 90+200\cdot 50=230\cdot T_3[/tex]
[tex]T_3=\frac{\dot{m_1}T_1+\dot{m_2}T_2}{\dot{m_3}}[/tex]
[tex]T_3=\frac{12700}{230}=55.21^{\circ}C[/tex]
