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4-24 A piston-cylinder device contains 50 kg of water at 250 kPa and 25°C. The cross-sectional area of the piston is 0.1 m?. Heat is now transferred to the water, causing part of it to evaporate and expand. When the volume reaches 0.2 m³, the piston reaches a linear spring whose spring constant is 100 kN/m. More heat is transferred to the water until the pis- ton rises 20 cm more. Determine (a) the final pressure and temperature and (b) the work done during this process. Als0, show the process on a P-V diagram. Answers: (a) 450 kPa, 147.9°C, (b) 44.5 kJ LA = 0.1 m2 H2O = 50 kg m = FIGURE P4-24

4-24 A piston-cylinder device contains 50 kg of water at 250 kPa and 25°C. The cross-sectional area of the piston is 0.1 m?. Heat is now transferred to the water, causing part of it to evaporate and expand. When the volume reaches 0.2 m³, the piston reaches a linear spring whose spring constant is 100 kN/m. More heat is transferred to the water until the pis- ton rises 20 cm more. Determine (a) the final pressure and temperature and (b) the work done during this process. Als0, show the process on a P-V diagram. Answers: (a) 450 kPa, 147.9°C, (b) 44.5 kJ LA = 0.1 m2 H2O = 50 kg m = FIGURE P4-24

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### Problem Statement 4-24 A piston–cylinder device contains 50 kg of water at an initial pressure of 250 kPa and an initial temperature of 25°C. The cross-sectional area of the piston is 0.1 m². Heat is added to the water, causing a portion of it to evaporate and expand. When the volume reaches 0.2 m³, the piston contacts a linear spring with a spring constant of 100 kN/m. Further heat is added until the piston rises an additional 20 cm. **Tasks:** 1. Determine the final pressure and temperature of the water. 2. Calculate the work done during this process. 3. Illustrate the process on a P-V (Pressure-Volume) diagram. **Answers:** (a) Final Pressure: 450 kPa, Final Temperature: 147.9°C (b) Work Done: 44.5 kJ ### Diagram Explanation **Figure P4-24 Description:** - The figure shows a vertical piston-cylinder setup. - At the base of the cylinder, there is water whose mass is specified as 50 kg. - The cross-sectional area of the piston is given as 0.1 m². - There is a spring attached to the top of the piston, depicted in a compressed state, indicating its engagement during the process. - The spring has a constant of 100 kN/m. - An arrow labeled "Q" represents the heat input to the system, entering the water at the bottom of the cylinder. ### Diagram Analysis - Initially, the piston is free to move without resistance until it reaches a volume of 0.2 m³. - Upon further expansion, the spring begins to compress, affecting the pressure inside the cylinder. - The process involves both heat addition and mechanical work performed against the spring as the piston moves upwards. ### Educational Context This problem provides an opportunity to apply thermodynamic principles, specifically the understanding of a piston-cylinder assembly involving phase change and work due to a spring force. It illustrates the use of P-V diagrams to conceptualize the relationship between pressure and volume changes during heat addition.
Transcribed Image Text:### Problem Statement 4-24 A piston–cylinder device contains 50 kg of water at an initial pressure of 250 kPa and an initial temperature of 25°C. The cross-sectional area of the piston is 0.1 m². Heat is added to the water, causing a portion of it to evaporate and expand. When the volume reaches 0.2 m³, the piston contacts a linear spring with a spring constant of 100 kN/m. Further heat is added until the piston rises an additional 20 cm. **Tasks:** 1. Determine the final pressure and temperature of the water. 2. Calculate the work done during this process. 3. Illustrate the process on a P-V (Pressure-Volume) diagram. **Answers:** (a) Final Pressure: 450 kPa, Final Temperature: 147.9°C (b) Work Done: 44.5 kJ ### Diagram Explanation **Figure P4-24 Description:** - The figure shows a vertical piston-cylinder setup. - At the base of the cylinder, there is water whose mass is specified as 50 kg. - The cross-sectional area of the piston is given as 0.1 m². - There is a spring attached to the top of the piston, depicted in a compressed state, indicating its engagement during the process. - The spring has a constant of 100 kN/m. - An arrow labeled "Q" represents the heat input to the system, entering the water at the bottom of the cylinder. ### Diagram Analysis - Initially, the piston is free to move without resistance until it reaches a volume of 0.2 m³. - Upon further expansion, the spring begins to compress, affecting the pressure inside the cylinder. - The process involves both heat addition and mechanical work performed against the spring as the piston moves upwards. ### Educational Context This problem provides an opportunity to apply thermodynamic principles, specifically the understanding of a piston-cylinder assembly involving phase change and work due to a spring force. It illustrates the use of P-V diagrams to conceptualize the relationship between pressure and volume changes during heat addition.
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