Does an Irreversible Adiabatic Process Defy the Equation PV^(gamma)=constant?

Click For Summary

Discussion Overview

The discussion revolves around the applicability of the equation PV^(gamma)=constant to irreversible adiabatic processes. Participants explore the conditions under which this equation holds true and the implications of irreversible processes in thermodynamics.

Discussion Character

  • Debate/contested
  • Technical explanation
  • Conceptual clarification

Main Points Raised

  • Some participants argue that an irreversible adiabatic process does not follow the equation PV^(gamma)=constant because it is not isentropic.
  • It is suggested that for the equation to apply, the ideal gas law must hold at all times, which requires thermodynamic equilibrium during the process.
  • One participant notes that a reversible adiabatic process must occur with a very small pressure difference between the gas and external pressure, allowing for equal work done in both directions.
  • Another viewpoint is presented that an irreversible adiabatic process occurs too rapidly for the ideal gas law (PV=nRT) to apply, due to kinetic energy factors in the gas.
  • A participant expresses a disagreement regarding the classification of processes as adiabatic when kinetic energy is lost to the surroundings during rapid expansion.

Areas of Agreement / Disagreement

Participants do not reach a consensus, as there are multiple competing views regarding the nature of irreversible adiabatic processes and their adherence to the equation PV^(gamma)=constant.

Contextual Notes

Limitations include the dependence on definitions of adiabatic processes and the assumptions regarding thermodynamic equilibrium and kinetic energy transfer.

asdf1
Messages
734
Reaction score
0
Why doesn't an irreversible adiabatic process follow the equation,
PV^(gamma)=constant?
 
Science news on Phys.org
asdf1 said:
Why doesn't an irreversible adiabatic process follow the equation,
PV^(gamma)=constant?

Although some people here (i.e. my friend Andrew Mason) are of another "school of knowledge", I must say an irreversible adiabatic process is not an isentropic one, and so it is not described by your equation.
 
Clausius2 said:
Although some people here (i.e. my friend Andrew Mason) are of another "school of knowledge", I must say an irreversible adiabatic process is not an isentropic one, and so it is not described by your equation.
For [itex]PV^\gamma = constant[/itex] to apply, the ideal gas law must apply at all times during the process. But this assumes that the system is at perfect thermodynamic equilibrium at all times during the process.

For an adiabatic gas expansion to be reversible, it must occur with an arbitrarily small pressure difference between the gas pressure and the external pressure. If this is the case, the work done by the gas in expanding ([itex]\int P_{gas}dv[/itex])is equal to the work done on the gas by the external pressure to return it to its original state ([itex]\int P_{ext}dv[/itex]) - hence it is reversible.

Typically an "irreversible adiabatic process" for an ideal gas is a process that occurs without exchange of heat with the surroundings but too rapidly for the relationship PV=nRT to apply during the process. The reason PV=nRT does not apply is because of the kinetic energy factor in the rapidly expanding or contracting gas.

My (mild) disagreement with friend Clausius2 is in calling all such processes adiabatic where kinetic energy is lost from the gas to the surroundings. If the gas expands rapidly and the resulting kinetic energy of the gas is ultimately transferred to the surroundings, I would say that the process is not adiabatic: heat (molecular kinetic energy) is effectively transferred to the surroundings.

AM
 
hmm... that makes sense~
thanks! :)
 

Similar threads

Undergrad Irreversible adiabatic processes & entropy change (clarification needed)
  • · Replies 22 ·
Replies
22
Views
6K
Undergrad Graphical difference between adiabatic and isothermal processes.
  • · Replies 1 ·
Replies
1
Views
4K
Undergrad Focus Problem for Entropy Change in Irreversible Adiabatic Process
  • · Replies 60 ·
3
Replies
60
Views
11K
Undergrad Adiabatic irreversible process vs adiabatic reversible
  • · Replies 1 ·
Replies
1
Views
2K
Undergrad Solving Adiabatic Process for Two Compartments
  • · Replies 1 ·
Replies
1
Views
2K
Query on Isentropic relationships (such as PV^gamma = constant)
  • · Replies 1 ·
Replies
1
Views
2K
High School Adiabatic or Isobaric process?
  • · Replies 61 ·
3
Replies
61
Views
7K
Graduate Entropy and Enthelpy for adiabatic process
  • · Replies 2 ·
Replies
2
Views
9K
Undergrad Adiabatic Process: Solving a Thermodynamics Problem
  • · Replies 14 ·
Replies
14
Views
3K
Graduate Why dU may not equals dW in free expansion?
  • · Replies 6 ·
Replies
6
Views
2K