Work done by a gas in a piston

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Discussion Overview

The discussion revolves around the work done by a gas in a piston when weights are suddenly removed. Participants explore the implications of this scenario on gas pressure, volume changes, and the nature of the expansion (reversible vs. irreversible). The conversation touches on theoretical models and equations relevant to thermodynamics.

Discussion Character

  • Debate/contested
  • Technical explanation
  • Mathematical reasoning

Main Points Raised

  • One participant suggests that the work done by the gas is the difference between the forces exerted by the gas and the atmosphere multiplied by the change in volume, questioning if the gas pressure can be assumed to instantaneously change to atmospheric pressure upon weight removal.
  • Another participant challenges the reasonableness of this assumption and suggests solving the equation ##PV^{\gamma}=nRT##.
  • A different participant points out that during an irreversible expansion, the gas pressure is not inversely proportional to its volume and that the pressure is not uniform within the cylinder.
  • It is noted that the work done by the gas can be determined if the external force at the piston face is known, as the gas pressure matches this external pressure.
  • Some participants argue that the equation mentioned is not valid for irreversible expansions and that the ideal gas law applies only in reversible conditions.
  • References to external links are made, indicating that the processes discussed in those links are explicitly reversible.
  • One participant acknowledges confusion regarding the distinction between reversible and irreversible processes, particularly in the context of removing weights from the piston.

Areas of Agreement / Disagreement

Participants express disagreement on the assumptions regarding gas pressure changes and the applicability of certain equations to irreversible expansions. There is no consensus on the validity of the initial assumptions or the interpretations of the equations involved.

Contextual Notes

Participants highlight limitations in the assumptions made about gas behavior during rapid changes and the conditions under which certain thermodynamic equations apply. The discussion remains focused on theoretical interpretations without resolving the underlying complexities.

goggles31
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Let's assume that weights are placed on a massless piston and below the piston is a gas. If we remove all the weights at once, the work done by the gas should be the difference between the forces exerted by the gas and the atmosphere multiplied by the change in volume. However, we know that the pressure exerted by a gas is inversely proportional to its volume and hence the work done is given by the area under a curve. Is it okay to assume that the pressure of the gas instantaneously changes to atmospheric pressure when the weights are removed, as in Figure 4.10 of the link given?

http://web.mit.edu/16.unified/www/FALL/thermodynamics/notes/node34.html
 
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I don't think that seems very reasonable. Try solving ##PV^{\gamma}=nRT##
 
goggles31 said:
Let's assume that weights are placed on a massless piston and below the piston is a gas. If we remove all the weights at once, the work done by the gas should be the difference between the forces exerted by the gas and the atmosphere multiplied by the change in volume. However, we know that the pressure exerted by a gas is inversely proportional to its volume and hence the work done is given by the area under a curve. Is it okay to assume that the pressure of the gas instantaneously changes to atmospheric pressure when the weights are removed, as in Figure 4.10 of the link given?

http://web.mit.edu/16.unified/www/FALL/thermodynamics/notes/node34.html
In an irreversible expansion, the pressure exerted by a gas on the piston is not inversely proportional to its volume. The gas pressure is not even uniform spatially within the cylinder during an irreversible expansion. Plus, the force is affected by viscous (dissipative) stresses in the gas such that the rate of change of volume also affects the force. However, the work that the gas does on the piston can be determined if we know the external force applied to the gas at the piston face (because the gas pressure matches the "external pressure" at the piston face).

For more details on this, see my two Physics Forums Insights articles: https://www.physicsforums.com/insights/understanding-entropy-2nd-law-thermodynamics/ and https://www.physicsforums.com/insights/reversible-vs-irreversible-gas-compressionexpansion-work/
 
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BiGyElLoWhAt said:
I don't think that seems very reasonable. Try solving ##PV^{\gamma}=nRT##
This equation is not valid for an irreversible expansion, or any other expansion for that matter. If the expansion is reversible, then the ideal gas law applies (exactly as it is always written).
 
Also, in the link, the processes are explicitly reversible.
 
BiGyElLoWhAt said:
Also, in the link, the processes are explicitly reversible.
Not for the cases where finite weights are suddenly removed from the piston.
 
Hmm... I see. Removing each small weight is what they're referring to as reversible. Sorry about that.
 
  • #10
BiGyElLoWhAt said:
Hmm... I see. Removing each small weight is what they're referring to as reversible. Sorry about that.
No problem. These things are always very confusing.
 

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