Gas Expansion in insulated cylinder (piston & Diaphragm)

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Discussion Overview

The discussion revolves around the analysis of gas expansion in an insulated cylinder divided by a diaphragm or a piston. Participants explore the thermodynamic implications of two cases: one involving a diaphragm (case A) and the other a piston (case B). The focus includes concepts of free expansion, work done on surroundings, and the nature of the processes involved, including isothermal and adiabatic conditions.

Discussion Character

  • Exploratory
  • Technical explanation
  • Debate/contested
  • Mathematical reasoning

Main Points Raised

  • Some participants question whether both cases can be classified as free expansion, particularly considering the nature of the piston in case B.
  • There is a discussion about the implications of a massless piston and whether it affects the expansion process.
  • Some participants propose that if the piston is connected to the outside, it would do work on the surroundings, altering the physics of the problem.
  • One participant suggests that case A is an irreversible free expansion process with no heat transfer or work done, leading to no change in internal energy and thus an isothermal process.
  • In contrast, case B is debated as potentially being an adiabatic expansion process, where work is done on the surroundings, and the final pressure is questioned.
  • Participants discuss the relationship between pressure, volume, and temperature changes in both cases, with some asserting that case B cannot be treated as free expansion.
  • There is uncertainty about whether case B can be assumed to be reversible, with some participants suggesting that the rate of expansion is a determining factor.
  • The ideal gas law is referenced to analyze the relationships between pressure, volume, and temperature in both cases.
  • Some participants express confusion regarding the temperature changes in case B compared to case A, particularly in relation to the nature of the expansion processes.

Areas of Agreement / Disagreement

Participants exhibit multiple competing views regarding the classification of the expansion processes, the implications of the piston being connected to the outside, and the nature of the temperature changes in both cases. The discussion remains unresolved with no consensus reached on several key points.

Contextual Notes

There are limitations regarding assumptions about the nature of the piston, the external conditions, and the definitions of free and adiabatic expansions. The discussion also reflects uncertainty about the rates of expansion and their impact on the reversibility of the processes.

  • #31
voko said:
Why is there no change in temperature in this case?



Consequently, what happens with temperature?


I am having problems with looking at this conceptually. I will try to take another crack at justifying case A. Since there's no heat transfer and work in case A, that means there's no change in internal temperature. For a perfect gas, internal temperature is only a function of temperature. Since there's no change in internal energy, there's no change in temperatre. Temperature and internal energy are directly correlated
 
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  • #32
pyroknife said:
Since there's no change in internal energy, there's no change in temperatre. Temperature and internal energy are directly correlated

And what does that imply for case B?
 
  • #33
voko said:
And what does that imply for case B?
Oh I see. Internal energy and temp would also be directly correlated for case B because the gas is still an ideal gas. There's no heat but there's a work output thus change in internal energy is negative, which implies change in temperature is negative (a decrease in temp from initial to final)!
 
  • #34
Correct. And what does lower final temperature imply for final pressure?
 
  • #35
voko said:
Correct. And what does lower final temperature imply for final pressure?
Sweet. Hmmm, wouldn't we have to know the change in temperature to determine whether the final pressure increase or decrease?

I forgot to mention the final volume is 6 times the original volume.

Let me work this out mathematically.

The left portion (1) has a volume 5x the volume of the right. I have use "f" index to denote final state rather than (2).
For case A:
P1V1=P_f*V_f, V_f=1/5V1+V1=6/5*V1
=>P_f=5/6*P1 (Decrease in pressure for case A)For case B:
P1V1/T1=P_f*V_f/T_f => P_f=5/6*P1*T_f/T1. The ratio T_f/T1 is less <1, thus P_f for case B is less than P_f for case A.
Is there any way to obtain the T_f/T1 ratio though?
 
Last edited:
  • #36
It is generally bad when one symbol means more than one thing, as is the case with your symbols labeled with "f". Your conclusion is correct, however.

I do not think it is possible to obtain final temperature/pressure in case B without making additional assumptions on the process.
 

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