**Question 5**By making mass balance and energy balance on the control volume, the computed value of the mass flow rate of the cold water, \( m_c \), in kg/s is:[Text Box for Answer] **Title: Analysis of Heat Exchange in an Insulated Mixing Chamber****Introduction**A hot-water stream at 90°C enters an insulated mixing chamber with a mass flow rate \(m_h = 0.75 \, \text{kg/s}\). This is mixed with a stream of cold water at 25°C in a steady-state, steady-flow process. The goal is for the mixture to exit the chamber at 45°C. **Diagram Explanation**- **Hot Water Inlet (1):** - Pressure (\(P_1\)) = 300 kPa - Temperature (\(T_1\)) = 90°C - Mass flow rate (\(m_h\)) = 0.75 kg/s- **Cold Water Inlet (2):** - Pressure (\(P_2\)) = 300 kPa - Temperature (\(T_2\)) = 25°C - Mass flow rate (\(m_c\)) = ?- **Mixed Warm Water Outlet (3):** - Pressure (\(P_3\)) = 300 kPa - Temperature (\(T_3\)) = 45°C - Mass flow rate (\(m_3\))**Conclusion**The mixing process shown in the schematic seeks to utilize energy balance for determining the unknown mass flow rate of the cold water to achieve the desired outlet temperature of 45°C. The system is modeled as an ideal, insulated condition, ensuring no heat loss to the surroundings. This is critical for applications requiring precise temperature control in thermal systems.

Answered: Image /qna-images/answer/05f5318a-d712-4e2d-80cc-a5202ab16f81.jpg

A hot-water stream at 90 °C enters an insulated mixing chamber with a mass flow rate of mh=0.75 kg/s where it is mixed with a stream of cold water at 25°C in a steady state steady flow process. It is desired that the mixture leaves the chamber at 45°C as shown in the Figure Hot water P₁=300 kPa T₁=90°C m-0.75 kg/s Cold water P=300 kPa T:=25%C m=? 2 Mixing Chamber Mixed warm water Ps-300 kPa T=45°C m3

A hot-water stream at 90 °C enters an insulated mixing chamber with a mass flow rate of mh=0.75 kg/s where it is mixed with a stream of cold water at 25°C in a steady state steady flow process. It is desired that the mixture leaves the chamber at 45°C as shown in the Figure Hot water P₁=300 kPa T₁=90°C m-0.75 kg/s Cold water P=300 kPa T:=25%C m=? 2 Mixing Chamber Mixed warm water Ps-300 kPa T=45°C m3

Elements Of Electromagnetics

7th Edition

ISBN:9780190698614

Author:Sadiku, Matthew N. O.

Publisher:Sadiku, Matthew N. O.

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Concept explainers

Work and Heat Transfer

It is generally related to thermal engineering which tells about the use, creation, conversion and transfer of heat energy between the systems. It is also considered that to transfer heat from one source to another, transfer of masses is also required. There are various mechanisms by which, transfer of heat takes place i.e. thermal conduction, convection, radiation or by change of phase. All these mechanisms have their own specific features which sometimes occur simultaneously within the same system.

Question

**Title: Analysis of Heat Exchange in an Insulated Mixing Chamber**

**Introduction**

A hot-water stream at 90°C enters an insulated mixing chamber with a mass flow rate \(m_h = 0.75 \, \text{kg/s}\). This is mixed with a stream of cold water at 25°C in a steady-state, steady-flow process. The goal is for the mixture to exit the chamber at 45°C.

**Diagram Explanation**

- **Hot Water Inlet (1):**
- Pressure (\(P_1\)) = 300 kPa
- Temperature (\(T_1\)) = 90°C
- Mass flow rate (\(m_h\)) = 0.75 kg/s

- **Cold Water Inlet (2):**
- Pressure (\(P_2\)) = 300 kPa
- Temperature (\(T_2\)) = 25°C
- Mass flow rate (\(m_c\)) = ?

- **Mixed Warm Water Outlet (3):**
- Pressure (\(P_3\)) = 300 kPa
- Temperature (\(T_3\)) = 45°C
- Mass flow rate (\(m_3\))

**Conclusion**

The mixing process shown in the schematic seeks to utilize energy balance for determining the unknown mass flow rate of the cold water to achieve the desired outlet temperature of 45°C. The system is modeled as an ideal, insulated condition, ensuring no heat loss to the surroundings. This is critical for applications requiring precise temperature control in thermal systems.

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