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4-124 A frictionless piston-cylinder device initially con- tains air at 100 kPa and 0.15 m³. At this state, a linear spring (Fx x) is touching the piston but exerts no force on it. The air is now heated to a final state of 0.45 m³ and 800 kPa. Deter- mine (a) the total work done by the air and (b) the work done against the spring. Also, show the process on a P-V diagram. Answers: (a) 135 kJ, (b) 105 kJ Air P₁ = 100 kPa 3 V₁ = 0.15 m³

4-124 A frictionless piston-cylinder device initially con- tains air at 100 kPa and 0.15 m³. At this state, a linear spring (Fx x) is touching the piston but exerts no force on it. The air is now heated to a final state of 0.45 m³ and 800 kPa. Deter- mine (a) the total work done by the air and (b) the work done against the spring. Also, show the process on a P-V diagram. Answers: (a) 135 kJ, (b) 105 kJ Air P₁ = 100 kPa 3 V₁ = 0.15 m³

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
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The answers are give as part a.)135 kJ and part b.)105kJ. Thank you for the help!
**Problem Statement** **4-124** A frictionless piston-cylinder device initially contains air at 100 kPa and 0.15 m³. At this state, a linear spring (\( F \propto x \)) is touching the piston but exerts no force on it. The air is now heated to a final state of 0.45 m³ and 800 kPa. Determine (a) the total work done by the air and (b) the work done against the spring. Also, show the process on a P-V diagram. **Answers:** (a) 135 kJ, (b) 105 kJ **Diagram Explanation** The diagram shows a piston-cylinder arrangement: - **Cylinder**: Contains air at an initial pressure (\( P_1 \)) of 100 kPa and volume (\( V_1 \)) of 0.15 m³. - **Piston**: A movable barrier that can slide up and down within the cylinder. - **Spring**: Positioned above the piston, initially exerting no force. The force exerted by the spring is proportional to its displacement (\( F \propto x \)). - **Air**: The working fluid that undergoes a thermodynamic process. Initially, the air has a pressure of 100 kPa and occupies a volume of 0.15 m³. It is heated until the volume expands to 0.45 m³ and the pressure reaches 800 kPa. The diagram visually represents these components, illustrating the initial conditions of the system. **P-V Diagram** Not depicted here, but the P-V diagram would show: - An initial point at 100 kPa and 0.15 m³. - A final point at 800 kPa and 0.45 m³. - The process path illustrating how the system transitions from the initial state to the final state, often involving two segments: one where the spring is not yet engaged, and a second where the spring begins to compress and exert force.
Transcribed Image Text:**Problem Statement** **4-124** A frictionless piston-cylinder device initially contains air at 100 kPa and 0.15 m³. At this state, a linear spring (\( F \propto x \)) is touching the piston but exerts no force on it. The air is now heated to a final state of 0.45 m³ and 800 kPa. Determine (a) the total work done by the air and (b) the work done against the spring. Also, show the process on a P-V diagram. **Answers:** (a) 135 kJ, (b) 105 kJ **Diagram Explanation** The diagram shows a piston-cylinder arrangement: - **Cylinder**: Contains air at an initial pressure (\( P_1 \)) of 100 kPa and volume (\( V_1 \)) of 0.15 m³. - **Piston**: A movable barrier that can slide up and down within the cylinder. - **Spring**: Positioned above the piston, initially exerting no force. The force exerted by the spring is proportional to its displacement (\( F \propto x \)). - **Air**: The working fluid that undergoes a thermodynamic process. Initially, the air has a pressure of 100 kPa and occupies a volume of 0.15 m³. It is heated until the volume expands to 0.45 m³ and the pressure reaches 800 kPa. The diagram visually represents these components, illustrating the initial conditions of the system. **P-V Diagram** Not depicted here, but the P-V diagram would show: - An initial point at 100 kPa and 0.15 m³. - A final point at 800 kPa and 0.45 m³. - The process path illustrating how the system transitions from the initial state to the final state, often involving two segments: one where the spring is not yet engaged, and a second where the spring begins to compress and exert force.
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