Understanding Isothermal Work: Solving the Gas Compression Problem

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Homework Help Overview

The discussion revolves around a homework problem related to isothermal work in the context of gas compression, specifically involving an ideal gas and the application of the ideal gas law. Participants are trying to understand how a specific temperature of 74 K was derived, contrasting it with another answer of 1500 K.

Discussion Character

  • Exploratory, Conceptual clarification, Problem interpretation, Assumption checking

Approaches and Questions Raised

  • Participants discuss the use of the ideal gas law and the implications of setting temperatures equal. There are inquiries about the derivation of formulas for isothermal work and whether certain assumptions, such as constant pressure, are valid in this context.

Discussion Status

The discussion is ongoing, with participants exploring different interpretations of the problem. Some have suggested looking at provided answers for guidance, while others express confusion about the lack of derivations for necessary formulas. There is acknowledgment of the course's algebra-based approach, which limits the use of calculus in solving the problem.

Contextual Notes

Participants note that the course does not cover calculus extensively, which affects their understanding of thermodynamics concepts. There is also mention of a specific formula for work that may not have been derived in class, leading to further questions about how to approach the problem without it.

member 731016
Homework Statement
please see below
Relevant Equations
PV = nRT
For this problem,
1680050652434.png

dose anybody please give me guidance how they got 74 K as the answer? Note that chat GPT dose not give the correct answer (it gives the temperature of the gas is 1500 K).

Many Thanks!
 
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This is a homework problem. You know the rules. Please show some work. I would also suggest that you look at the chat GPT answer and see whether there is anything you can use.
 
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kuruman said:
This is a homework problem. You know the rules. Please show some work. I would also suggest that you look at the chat GPT answer and see whether there is anything you can use.
Thank you for your reply @kuruman!

Since this is an ideal gas, I though I could you the ideal gas law. So as far as I got was setting the temperatures equal ##\frac{P_iV_i}{nR} = \frac{P_fV_i}{5nR}## which gave ##5P_i = P_f##.

Many thanks!
 
If you use calculus in your course, then your professor or textbook has probably derived a formula for the work associated with a quasi-static, isothermal expansion/compression of an ideal gas.
 
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TSny said:
If you use calculus in your course, then your professor or textbook has probably derived a formula for the work associated with a quasi-static, isothermal expansion/compression of an ideal gas.
Thank you for your reply @TSny!

No sorry, this course is algebras based. We did not do the calculus parts and a lot of the thermo so stuff it not really making sense very much.

Many thanks!
 
TSny said:
If you use calculus in your course, then your professor or textbook has probably derived a formula for the work associated with a quasi-static, isothermal expansion/compression of an ideal gas.
Its an intro physics course so we cover dimensional analysis then thermo, and eventually mechanics and waves.
 
Nevermind, I think I really overthought this simple problem. Sorry.
 
Callumnc1 said:
Its an intro physics course so we cover dimensional analysis then thermo, and eventually mechanics and waves.
Ok. I wonder if the formula for isothermal work was given to you without a derivation. I don't see how to work the problem without this formula.
 
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TSny said:
Ok. I wonder if the formula for isothermal work was given to you without a derivation. I don't see how to work the problem without this formula.
Thank you for your reply @TSny! Yeah, the only way I now realize that this problem to be solved is if we assume pressure it not constant, which then I have to use the work integral in terms of differential volume which was not shown in class. We were only shown ##W = P(V_2 - V_1)## which I now know assumes the special case where the pressure is constant.
 
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