Gas is contained in a vertical piston-cylinder apparatus as shown below. The piston is fixed to a massless rigid structure (bar connected to a plate). This structure is attached to support weights if added. Initially there is no mass on the plate such that the initial gas pressure is P Patm ft. A mass mw=720 lbm is placed on the plate which causes the piston to compress the The compression process of the gas follows the relationship PV = C. Also for the process the change in energy of the gas is zero. Determine = 14.7 psia and the initial gas volume is V =1 ft. The piston surface area Ap = 1 %3D gas. %3D Determine a) the piston displacement, Ax [ft]. b) the work done on the gas, Wga: [ft-lbf], and c) the heat transfer from the gas. Q12 [Btu].
Gas is contained in a vertical piston-cylinder apparatus as shown below. The piston is fixed to a massless rigid structure (bar connected to a plate). This structure is attached to support weights if added. Initially there is no mass on the plate such that the initial gas pressure is P Patm ft. A mass mw=720 lbm is placed on the plate which causes the piston to compress the The compression process of the gas follows the relationship PV = C. Also for the process the change in energy of the gas is zero. Determine = 14.7 psia and the initial gas volume is V =1 ft. The piston surface area Ap = 1 %3D gas. %3D Determine a) the piston displacement, Ax [ft]. b) the work done on the gas, Wga: [ft-lbf], and c) the heat transfer from the gas. Q12 [Btu].
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
Gas is contained in a vertical piston-cylinder apparatus as shown below. The piston is fixed to a massless rigid structure (bar connected to a plate). This structure is attached to support weights if added. Initially, there is no mass on the plate such that the initial gas pressure is \( P_1 = P_{\text{atm}} = 14.7 \) psia and the initial gas volume is \( V_1 = 1 \, \text{ft}^3 \). The piston surface area \( A_p = 1 \, \text{ft}^2 \). A mass \( m_w = 720 \, \text{lbm} \) is placed on the plate which causes the piston to compress the gas. The compression process of the gas follows the relationship \( PV = C \). Also, for the process, the change in energy of the gas is zero. Determine:
a) the piston displacement, \( \Delta x \) [ft].
b) the work done on the gas, \( W_{\text{gas}} \) [ft-lbf].
c) the heat transfer from the gas, \( Q_{12} \) [Btu].
### Diagram Explanation
The diagram features the following components:
- **Massless Plate:** Located at the top, attached to the massless rigid structure.
- **Mass \( m_w \):** Shown on the plate causing compression.
- **Massless Rigid Structure:** Extends vertically to support the piston.
- **Piston:** Connected to the structure, it compresses the gas when the mass is added.
- **Gas Cylinder:** Contains the gas, represented inside the rectangular box.
- **Initial Parameters:** \( P_{\text{atm}} \) is the atmospheric pressure acting on the system.
- **Piston Surface Area \( A_p \):** Displayed as affecting the gas in the cylinder.
- **Process Indicators:**
- \( x > 0 \): Represents displacement direction of the piston.
- \( Q_{12} \): Indicates heat transfer from the gas.
The objective is to calculate the piston displacement, work done on the gas, and heat transfer resulting from the applied mass and the ensuing compression process, adhering to the provided conditions and relationships.](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F22ca1a07-91f9-4fe1-8e4a-b558cd554103%2F21809f6f-9d02-4514-80b2-a7837b232840%2Fgxsed4h_processed.jpeg&w=3840&q=75)
Transcribed Image Text:### Problem Statement
Gas is contained in a vertical piston-cylinder apparatus as shown below. The piston is fixed to a massless rigid structure (bar connected to a plate). This structure is attached to support weights if added. Initially, there is no mass on the plate such that the initial gas pressure is \( P_1 = P_{\text{atm}} = 14.7 \) psia and the initial gas volume is \( V_1 = 1 \, \text{ft}^3 \). The piston surface area \( A_p = 1 \, \text{ft}^2 \). A mass \( m_w = 720 \, \text{lbm} \) is placed on the plate which causes the piston to compress the gas. The compression process of the gas follows the relationship \( PV = C \). Also, for the process, the change in energy of the gas is zero. Determine:
a) the piston displacement, \( \Delta x \) [ft].
b) the work done on the gas, \( W_{\text{gas}} \) [ft-lbf].
c) the heat transfer from the gas, \( Q_{12} \) [Btu].
### Diagram Explanation
The diagram features the following components:
- **Massless Plate:** Located at the top, attached to the massless rigid structure.
- **Mass \( m_w \):** Shown on the plate causing compression.
- **Massless Rigid Structure:** Extends vertically to support the piston.
- **Piston:** Connected to the structure, it compresses the gas when the mass is added.
- **Gas Cylinder:** Contains the gas, represented inside the rectangular box.
- **Initial Parameters:** \( P_{\text{atm}} \) is the atmospheric pressure acting on the system.
- **Piston Surface Area \( A_p \):** Displayed as affecting the gas in the cylinder.
- **Process Indicators:**
- \( x > 0 \): Represents displacement direction of the piston.
- \( Q_{12} \): Indicates heat transfer from the gas.
The objective is to calculate the piston displacement, work done on the gas, and heat transfer resulting from the applied mass and the ensuing compression process, adhering to the provided conditions and relationships.
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