Heat transaction of a non-ideal gas

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Discussion Overview

The discussion centers on calculating heat interactions of non-ideal gases during isobaric and isochoric processes. Participants explore the relationship between internal energy, enthalpy, and heat capacities, as well as the implications of using Taylor series expansions in these calculations.

Discussion Character

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

Main Points Raised

  • One participant seeks to understand how to calculate heat interactions for non-ideal gases, specifically in isobaric and isochoric processes, referencing the dependence of internal energy on temperature and volume.
  • Another participant questions the use of heat capacities as functions of temperature and pressure, and whether the discussion pertains to actual gases or models like Van der Waals.
  • There is a suggestion that for specific gases, actual parameter values may be necessary rather than relying on general formulas.
  • One participant confirms the desire for an equation that expresses changes in internal energy in terms of known functions like heat capacity and p-v-T behavior.
  • A later post reiterates the need for an equation to calculate changes in internal energy, confirming the earlier participant's request.
  • Another participant provides a specific equation from thermodynamics relating changes in internal energy to temperature and volume changes.
  • There is a discussion about accessing relevant literature, with one participant suggesting that other articles on the topic may be available for free.

Areas of Agreement / Disagreement

Participants express varying views on the best approach to calculating heat interactions for non-ideal gases, with some advocating for the use of heat capacities and others questioning the applicability of models versus actual gases. The discussion remains unresolved regarding the best methods and resources for these calculations.

Contextual Notes

Participants mention the need for specific parameter values for certain gases, indicating potential limitations in using general formulas. There is also uncertainty regarding the accessibility of relevant literature.

Uthpala Kaushalya
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Here I want to know how to find the heat interactions of non-ideal gases in the following processes.
1. Isobaric process
2. Isochoric process

I know that internal energy U depends on temperature and volume. And the enthalpy depends on temperature and pressure.
How calculation of heat transaction can be calculated? and what's the connection between following taylor series expansion with calculating the heat interaction.

U(T,V)
U(T+T, V+V) = U(T,V) + ∂u/∂ t |v * T + ∂u/∂v |T * V + Higher Terms
 
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Why don't use the heat capacities of the gases, as functions of T and P?
Are talking about actual gases or just about a model of non-ideal gas (like Van der Waals)?
If it's a specific gas (like nitrogen) you may need to find some actual values of parameters for that gas rather than using a general formula.
Here is a paper that may help.
http://journals.aps.org/pr/pdf/10.1103/PhysRev.34.1615
 
Last edited by a moderator:
You would like to have an equation for calculating the changes internal energy with changes in temperature and volume for a non-ideal gas. Is that correct? In this equation, you would like everything expressed in terms of known functions like heat capacity and p-v-T behavior?
 
Chestermiller said:
You would like to have an equation for calculating the changes internal energy with changes in temperature and volume for a non-ideal gas. Is that correct? In this equation, you would like everything expressed in terms of known functions like heat capacity and p-v-T behavior?
Yes :)
 
nasu said:
Why don't use the heat capacities of the gases, as functions of T and P?
Are talking about actual gases or just about a model of non-ideal gas (like Van der Waals)?
If it's a specific gas (like nitrogen) you may need to find some actual values of parameters for that gas rather than using a general formula.
Here is a paper that may help.
http://journals.aps.org/pr/pdf/10.1103/PhysRev.34.1615
This article cannot be read. Should I buy this?
 
Last edited by a moderator:
No, you should be able to find other articles that have free access. I don't think this is a very rare topic.
 
The following equation is in every thermo book:
$$dU=C_vdT-\left[P-T\left(\frac{\partial P}{\partial T}\right)_V\right]dV$$
 

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