Introduction to Chemical Engineering Thermodynamics
8th Edition
ISBN: 9781259696527
Author: J.M. Smith Termodinamica en ingenieria quimica, Hendrick C Van Ness, Michael Abbott, Mark Swihart
Publisher: McGraw-Hill Education
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The answer should be W~=1900j/mol
I have posted this question but can you explain how to get that value of work.I used vdw EOS
![**Problem Statement:**
One mole of methane in a piston-cylinder system undergoes an adiabatic compression from an initial state (P1 = 0.5 bar, V1 = 0.05 m³/mol) to a final state (P2 = 10 bar, V2 = 0.003 m³/mol). How much work is done on the system?
**Explanation:**
- A **piston-cylinder system** is a common apparatus in thermodynamics used to analyze the behavior of gases under various processes.
- **Adiabatic compression** means that no heat is exchanged with the surroundings during the process.
- **Initial state:** When the process begins, the pressure (\(P1\)) is 0.5 bar, and the volume (\(V1\)) is 0.05 m³/mol.
- **Final state:** At the end of the process, the pressure (\(P2\)) is 10 bar, and the volume (\(V2\)) is 0.003 m³/mol.
To determine the work done on the system during this adiabatic process, we use the formula for adiabatic processes:
\[ W = \dfrac{P1V1 - P2V2}{\gamma - 1} \]
Where \(\gamma\) (gamma) is the adiabatic index or heat capacity ratio (Cp/Cv) of methane. For methane, \(\gamma\) is approximately 1.31.
Insert the known values into the formula to calculate the work done on the system.](https://content.bartleby.com/qna-images/question/44dce5c9-bcec-4e4b-a98e-07662a0f3f15/bc8b545f-b447-43fa-bdde-44da46b6d3e6/csn5bgk.png)
Transcribed Image Text:**Problem Statement:**
One mole of methane in a piston-cylinder system undergoes an adiabatic compression from an initial state (P1 = 0.5 bar, V1 = 0.05 m³/mol) to a final state (P2 = 10 bar, V2 = 0.003 m³/mol). How much work is done on the system?
**Explanation:**
- A **piston-cylinder system** is a common apparatus in thermodynamics used to analyze the behavior of gases under various processes.
- **Adiabatic compression** means that no heat is exchanged with the surroundings during the process.
- **Initial state:** When the process begins, the pressure (\(P1\)) is 0.5 bar, and the volume (\(V1\)) is 0.05 m³/mol.
- **Final state:** At the end of the process, the pressure (\(P2\)) is 10 bar, and the volume (\(V2\)) is 0.003 m³/mol.
To determine the work done on the system during this adiabatic process, we use the formula for adiabatic processes:
\[ W = \dfrac{P1V1 - P2V2}{\gamma - 1} \]
Where \(\gamma\) (gamma) is the adiabatic index or heat capacity ratio (Cp/Cv) of methane. For methane, \(\gamma\) is approximately 1.31.
Insert the known values into the formula to calculate the work done on the system.
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