Question

Two streams of water are mixed in an insulated container to form a third stream leaving the container. The first stream has a flow rate of 30 kg/s and a temperature of 90°C. The flow rate of the second stream is 200 kg/s, and its temperature is 50°C. What is the temperature of the third stream?

Answer 1

Answer:
`T_3=55.21^(\circ)`

Step-by-step explanation:

Given

mass of stream 1 is
`\dot{m_1}=30 kg/s`

Temperature
`T_1=90^(\circ)C`

mass of stream
`\dot{m_2}=200 kg/s`

Temperature
`T_2=50^(\circ)C`

mass of third stream
`\dot{m_3}`

`\dot{m_1}+\dot{m_2}=\dot{m_3}`

`30+200=\dot{m_3}`

`\dot{m_3}=230 kg/s`

Balancing Energy

`\dot{m_1}h_1+\dot{m_2}h_2=\dot{m_3}h_3`

`\dot{m_1}T_1+\dot{m_2}T_2=\dot{m_3}T_3`

`30\cdot 90+200\cdot 50=230\cdot T_3`

`T_3=\frac{\dot{m_1}T_1+\dot{m_2}T_2}{\dot{m_3}}`

`T_3=(12700)/(230)=55.21^(\circ)C`