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In the figure a rigid tank is shown, which is divided into two rooms by a membrane, both containing water. Room A is at 250 kPa, v = 0.5 m³/kg, VA = 1 m³, and room B contains 3.5 kg at 0.6 MPa, 325°C. The membrane now ruptures and heat transfer between the tank and the surroundings takes place, so the water comes to a uniform state at 100°C. Find the heat transfer between the tank and the surroundings during the process.

In the figure a rigid tank is shown, which is divided into two rooms by a membrane, both containing water. Room A is at 250 kPa, v = 0.5 m³/kg, VA = 1 m³, and room B contains 3.5 kg at 0.6 MPa, 325°C. The membrane now ruptures and heat transfer between the tank and the surroundings takes place, so the water comes to a uniform state at 100°C. Find the heat transfer between the tank and the surroundings during the process.

Elements Of Electromagnetics
Elements Of Electromagnetics
7th Edition
ISBN:9780190698614
Author:Sadiku, Matthew N. O.
Publisher:Sadiku, Matthew N. O.
ChapterMA: Math Assessment
Section: Chapter Questions
Problem 1.1MA
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### Title: Heat Transfer in a Rigid Tank #### Problem Description: In the figure, a rigid tank is shown, which is divided into two rooms by a membrane, both containing water. - Room A is at 250 kPa, \( v = 0.5 \, \text{m}^3/\text{kg} \), \( V_A = 1 \, \text{m}^3 \). - Room B contains 3.5 kg of water at 0.6 MPa, 325°C. The membrane now ruptures, and heat transfer between the tank and the surroundings takes place, so the water comes to a uniform state at 100°C. #### Objective: Find the heat transfer between the tank and the surroundings during the process. #### Explanation of Diagram: The diagram consists of a rectangular rigid tank divided into two rooms labeled A and B by a membrane. - Room A is on the left side of the membrane. - Room B is on the right side of the membrane. Both rooms contain water, and the properties of the water in each room are provided in the problem statement. ### Solution Approach: To solve this problem, you can follow these general steps: 1. **Determine Initial States:** - **Room A:** Using given initial state (250 kPa, \( v = 0.5 \, \text{m}^3/\text{kg} \)). - **Room B:** Using given initial state (0.6 MPa, 325°C). 2. **Calculate Total Mass and Volume:** - Find the mass of water in both rooms using density and volume. - Total mass, \( m_{total} = m_A + m_B \). - Total volume, \( V_{total} \). 3. **Find Final State Properties:** - At 100°C, use steam tables to find specific volume of water. 4. **Energy Balance:** - Use energy conservation principles. - Calculate the internal energy before and after the membrane ruptures. 5. **Calculate Heat Transfer:** - Using the first law of thermodynamics to determine the heat transfer to the surroundings. This detailed solution approach can be implemented using specific thermodynamic equations and steam tables to find the necessary properties. ### Educational Note: This problem involves important concepts in thermodynamics such as phase changes, specific volumes, energy balance, and heat transfer. It serves to
Transcribed Image Text:### Title: Heat Transfer in a Rigid Tank #### Problem Description: In the figure, a rigid tank is shown, which is divided into two rooms by a membrane, both containing water. - Room A is at 250 kPa, \( v = 0.5 \, \text{m}^3/\text{kg} \), \( V_A = 1 \, \text{m}^3 \). - Room B contains 3.5 kg of water at 0.6 MPa, 325°C. The membrane now ruptures, and heat transfer between the tank and the surroundings takes place, so the water comes to a uniform state at 100°C. #### Objective: Find the heat transfer between the tank and the surroundings during the process. #### Explanation of Diagram: The diagram consists of a rectangular rigid tank divided into two rooms labeled A and B by a membrane. - Room A is on the left side of the membrane. - Room B is on the right side of the membrane. Both rooms contain water, and the properties of the water in each room are provided in the problem statement. ### Solution Approach: To solve this problem, you can follow these general steps: 1. **Determine Initial States:** - **Room A:** Using given initial state (250 kPa, \( v = 0.5 \, \text{m}^3/\text{kg} \)). - **Room B:** Using given initial state (0.6 MPa, 325°C). 2. **Calculate Total Mass and Volume:** - Find the mass of water in both rooms using density and volume. - Total mass, \( m_{total} = m_A + m_B \). - Total volume, \( V_{total} \). 3. **Find Final State Properties:** - At 100°C, use steam tables to find specific volume of water. 4. **Energy Balance:** - Use energy conservation principles. - Calculate the internal energy before and after the membrane ruptures. 5. **Calculate Heat Transfer:** - Using the first law of thermodynamics to determine the heat transfer to the surroundings. This detailed solution approach can be implemented using specific thermodynamic equations and steam tables to find the necessary properties. ### Educational Note: This problem involves important concepts in thermodynamics such as phase changes, specific volumes, energy balance, and heat transfer. It serves to
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