3) A frictionless piston-cylinder device contains 3 m3 of a gas at 200 kPa and 300 K. The gas is now compressed slowly following the equation PV12 = constant until it reaches 500 K. Determine the boundary work of this process.
3) A frictionless piston-cylinder device contains 3 m3 of a gas at 200 kPa and 300 K. The gas is now compressed slowly following the equation PV12 = constant until it reaches 500 K. Determine the boundary work of this process.
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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![**Problem Statement:**
A frictionless piston-cylinder device contains 3 m³ of a gas at 200 kPa and 300 K. The gas is now compressed slowly following the equation PV^1.2 = constant until it reaches 500 K. Determine the boundary work of this process.
**Explanation:**
The problem involves a piston-cylinder setup where the gas inside undergoes compression. The process follows a polytropic process, indicated by the relation PV^1.2 = constant. In such a process, the relationship between pressure (P) and volume (V) is defined by a polytropic exponent, which in this case is 1.2.
Key parameters provided are:
- Initial volume (V₁) = 3 m³
- Initial pressure (P₁) = 200 kPa
- Initial temperature (T₁) = 300 K
- Final temperature (T₂) = 500 K
- Polytropic exponent (n) = 1.2
To find the boundary work, the process typically involves using the formula for work done during a polytropic process, which considers changes in pressure and volume.
**Steps for Solution (Not solving here, just explaining):**
1. Use the ideal gas law to find the mass of the gas, if required.
2. Apply the relation PV^n = constant to calculate the final pressure and volume.
3. Use the formula for boundary work during a polytropic process:
\[
W = \frac{P_2 V_2 - P_1 V_1}{1 - n}
\]
where P and V are the pressures and volumes at initial (1) and final (2) states.
This setup and problem-type are useful for understanding thermodynamic processes and the application of energy equations in mechanical engineering.](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F8091f38e-d53b-4700-9beb-62676d968b37%2F3c0c488c-bcf7-4c15-bbc6-cefc2f572eab%2Fl1qamlh_processed.png&w=3840&q=75)
Transcribed Image Text:**Problem Statement:**
A frictionless piston-cylinder device contains 3 m³ of a gas at 200 kPa and 300 K. The gas is now compressed slowly following the equation PV^1.2 = constant until it reaches 500 K. Determine the boundary work of this process.
**Explanation:**
The problem involves a piston-cylinder setup where the gas inside undergoes compression. The process follows a polytropic process, indicated by the relation PV^1.2 = constant. In such a process, the relationship between pressure (P) and volume (V) is defined by a polytropic exponent, which in this case is 1.2.
Key parameters provided are:
- Initial volume (V₁) = 3 m³
- Initial pressure (P₁) = 200 kPa
- Initial temperature (T₁) = 300 K
- Final temperature (T₂) = 500 K
- Polytropic exponent (n) = 1.2
To find the boundary work, the process typically involves using the formula for work done during a polytropic process, which considers changes in pressure and volume.
**Steps for Solution (Not solving here, just explaining):**
1. Use the ideal gas law to find the mass of the gas, if required.
2. Apply the relation PV^n = constant to calculate the final pressure and volume.
3. Use the formula for boundary work during a polytropic process:
\[
W = \frac{P_2 V_2 - P_1 V_1}{1 - n}
\]
where P and V are the pressures and volumes at initial (1) and final (2) states.
This setup and problem-type are useful for understanding thermodynamic processes and the application of energy equations in mechanical engineering.
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