Finding pressure increase required to impart 1J of work

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Discussion Overview

The discussion revolves around estimating the pressure increase required to impart 1 J of mechanical work in the reversible compression of 1 mol of silver and alumina at room temperature. Participants explore the application of relevant equations and seek clarification on unit conversions and assumptions related to the problem.

Discussion Character

  • Homework-related
  • Mathematical reasoning

Main Points Raised

  • One participant presents the problem statement and equations related to mechanical work and volume changes, expressing difficulty in finding a solution.
  • Another participant confirms the correctness of the equation involving pressure and suggests substituting numerical values, assuming a starting pressure of 1 atm.
  • A participant inquires whether the same equation can be applied to part (b) of the problem, noting that it does not specify mechanical work or reversibility.
  • There is a request for a solution to the problem, which is met with a reminder of forum rules against providing direct solutions.
  • A participant raises a question about necessary unit conversions for molar volume and mentions discrepancies in beta values for silver, seeking clarification on the differences in molar volumes provided.

Areas of Agreement / Disagreement

Participants generally agree on the use of the equation for calculating pressure increase but express uncertainty regarding its application to different parts of the problem and the need for unit conversions. The discussion remains unresolved regarding the specific numerical answers and the application of the equations.

Contextual Notes

Participants mention various assumptions, such as the starting pressure and the nature of the work being done, but these assumptions are not universally agreed upon. There is also uncertainty regarding the appropriate unit conversions and the interpretation of different molar volumes.

geobot
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Homework Statement


a) Estimate the pressure increase required to impart 1 J of mechanical work in reversibly compressing 1 mol of silver at room temperature.
b) What pressure rise would be required to impart 1 J of work to 1 mol of alumina at room temperature? For AL2O3 take the molar volume to be 25.715 (cc mol^-1) and Beta= 8.0 x 10^-7 (atm)^-1

Homework Equations


mechanical work = -PdV
dV=V.alpha.dT - V.beta.dP
(maybe: dU = (Cp - PV.alpha)dT + V(P.beta - T.alpha)dP )

The Attempt at a Solution


I have tried and tried to come up with a solution but I just can't figure it out.
See attached jpg.
I would appreciate any thoughts on the question
 

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Your equation in the snapshot involving P's is correct. Just substitute numbers into it. Assume that the starting pressure is 1 atm.

Chet
 
Chestermiller said:
Your equation in the snapshot involving P's is correct. Just substitute numbers into it. Assume that the starting pressure is 1 atm.

Chet

Thank you, can I use that equation for part (b) as well? It does not specify that it is mechanical work or reversible there.
 
geobot said:
Thank you, can I use that equation for part (b) as well? It does not specify that it is mechanical work or reversible there.
Same as (a).
 
Chestermiller said:
Same as (a).
Oh wow, I've been really over thinking this question it seems! thanks again!
 
can I have a solution to this problem?
 
Jairaj Joshi said:
can I have a solution to this problem?
Nope. That's contrary to Physics Forum rules (you should read the guidelines). If you wish to solve this problem and you can't glean enough hints from the current thread's content then you can show your own attempt and present what part you don't understand, or start a new, separate thread and show your attempt there.
 
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Is there any unit conversions that need to be done if my molar volume is given in cc/mol I thought I might need to convert to m^3. The beta value for silver given in my textbook is 9e7 atm^-1, and the molar volume is given as V^S= 10.27 cc/mol, but there is also a V^L=11.54 cc/mol, and I'm not sure of the difference. I know this is an old thread, but any help would be greatly appreciated. I came to the same equation, but cannot get a correct answer.
 

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