Fundamental thermo systems problem

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Homework Help Overview

The discussion revolves around a thermodynamics problem involving the expansion of a fluid in a cylinder behind a piston. The specific conditions include an initial pressure of 3 bar and a specific volume of 0.18 m3/kg, with a reversible expansion to a pressure of 0.6 bar governed by the relationship p = c/v².

Discussion Character

  • Exploratory, Mathematical reasoning

Approaches and Questions Raised

  • Participants discuss the relationship between pressure, volume, and work done during the expansion process. There are attempts to derive the work done using calculus and the provided equations, with some participants expressing uncertainty about the steps needed to arrive at the known answer.

Discussion Status

The discussion is ongoing, with participants sharing their approaches to calculating the work done. Some guidance on the mathematical steps has been offered, but there is no explicit consensus on the method to reach the final answer.

Contextual Notes

There is mention of potential issues with sharing mathematical notation, which may affect the clarity of the discussion. Additionally, one participant indicates a need for a break after a long study session, suggesting a focus on self-care amidst the problem-solving process.

kik369
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1. Unit mass of a fluid at a pressure of 3 bar, and with a specific volume of 0.18 m3/kg, contained in a cylinder behind a piston expands reversibly to a pressure of 0.6 bar according to the law p = c/v2, where c is a constant. Calculate the work done during the process.
2. P1V1=P2V2
3. I know that the answer is 29.82 J/kg out of the system, but how to get it?
 
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c=p1*v12 but work=∫p*dv=∫c/v2*dv=c∫dv/v2 the rest is basic calculus. The answer units should be kj/kg
 
c=Subscript[p, 1]*Subsuperscript[v, 1, 2] but work = \[Integral]p \[DifferentialD]v =\[Integral]c/v^2 \[DifferentialD]v = c \[Integral]1/v^2 \[DifferentialD]v the rest is basic calc. I believe the answer units is KJ/Kg
 
Guess I can't copy mathematica text into the message box
 
Thank you! I'll go through this tomorrow. I've been working on these problems the whole day. It is time for me to take a break. I appreciate the reply.
 

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