Why Use Constant Volume for This Adiabatic Equation?

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    Adiabatic equation
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Discussion Overview

The discussion revolves around the use of constant volume in an adiabatic equation, particularly in relation to the internal energy of a gas and its heat capacity. Participants explore the implications of constant volume versus constant pressure in thermodynamic processes, focusing on ideal gases.

Discussion Character

  • Debate/contested
  • Technical explanation
  • Conceptual clarification

Main Points Raised

  • Some participants assert that the equation is written in constant volume because it relates to the internal energy of the gas.
  • Others express skepticism about the appropriateness of using internal energy for heat capacity in constant volume, arguing that if the process is not at constant volume, the change in internal energy should be zero.
  • One participant suggests that constant pressure might be more reasonable for the adiabatic process, as work is done on the system.
  • Another participant claims that the effect of volume on internal energy is only significant in diabatic processes, stating that in adiabatic processes with constant volume, the work done is zero and thus the change in internal energy is also zero.
  • A later reply challenges the previous claim, stating that the internal energy of an ideal gas depends solely on temperature, regardless of volume.
  • Some participants reference external sources to support their arguments regarding the relationship between internal energy, temperature, and volume.

Areas of Agreement / Disagreement

Participants do not reach a consensus, as multiple competing views regarding the relationship between internal energy, heat capacity, and the conditions of the process remain. Disagreement exists on whether constant volume is appropriate for the adiabatic equation.

Contextual Notes

There are unresolved assumptions regarding the definitions of constant volume and constant pressure in the context of adiabatic processes, as well as the implications of these conditions on internal energy changes.

abdossamad2003
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Why is this equation (red sign) written in constant volume and not in constant pressure?
Screenshot 2023-11-07 20.46.13.png
 
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Because this is what counts for the internal energy of the gas.
 
I was not convinced why internal energy should be written for heat capacity in constant volume. This process does not take place in constant volume, and if it is in constant volume, the change in internal energy must be zero.
 
The work is done on the adiabatic system, that is, it is not in constant volume, in my opinion, constant pressure seems more reasonable
 
What is your understanding of the effect of volume on the internal energy of an ideal gas?
 
The effect of volume on the internal energy is meaningful only in diabatic processes, for example, when heat is added to the system at a constant volume and the internal energy increases, but in adiabatic processes, when the volume is constant, the work done on the system is zero and the incoming heat is zero, as a result of the change in energy Internal is zero.
 
abdossamad2003 said:
The effect of volume on the internal energy is meaningful only in diabatic processes, for example, when heat is added to the system at a constant volume and the internal energy increases, but in adiabatic processes, when the volume is constant, the work done on the system is zero and the incoming heat is zero, as a result of the change in energy Internal is zero.
This is totally incorrect. Irrespective of the process, the internal energy of an ideal gas depends only on temperature, and not volume.
 
Last edited:
abdossamad2003 said:
I was not convinced why internal energy should be written for heat capacity in constant volume. This process does not take place in constant volume, and if it is in constant volume, the change in internal energy must be zero.
See, e.g., here: https://en.wikipedia.org/wiki/Internal_energy#Internal_energy_of_the_ideal_gas. ##C_V## is the coefficient of proportionality between internal energy on one hand and number of moles and temperature of the gas on the other hand.
 

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