Isothermal Processes: Ideal Gas Equation and Doubts Explained

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Discussion Overview

The discussion revolves around the relationship between isothermal processes and the ideal gas equation, specifically questioning whether all isothermal processes can be described by the equation PV=mRT. Participants explore the implications of this relationship in closed systems, the nature of real gases, and the conditions under which the ideal gas law applies.

Discussion Character

  • Debate/contested
  • Technical explanation
  • Conceptual clarification

Main Points Raised

  • Some participants propose that in closed systems, isothermal processes can be described by the ideal gas equation PV=mRT, as temperature, R, and mass remain constant.
  • Others argue that real gases do not strictly obey the ideal gas law, and that solids and liquids are excluded from this law's applicability.
  • A later reply questions whether it is possible for a polytropic process with an index of 1 to be described by an equation other than mRT.
  • Another participant raises the issue of irreversible processes, suggesting that while the outer boundary may maintain constant temperature, the internal temperature can vary, complicating the definition of isothermal processes.
  • Some participants express confusion about the relationship between ideal gases and polytropic processes, particularly in the context of specific examples from external links.
  • One participant emphasizes the need for clarity regarding whether isothermal polytropic processes can have indices other than 1.
  • A response suggests that for constant temperature reversible expansions, the ideal gas assumption is necessary for satisfying the polytropic equation.
  • Another participant advises against spending time on speculative questions, suggesting a focus on practical thermodynamics problem-solving instead.

Areas of Agreement / Disagreement

Participants do not reach a consensus on the relationship between isothermal processes and the ideal gas equation, with multiple competing views and uncertainties remaining about the applicability of the ideal gas law to real gases and polytropic processes.

Contextual Notes

Participants express uncertainty regarding the definitions and applicability of the ideal gas law in various contexts, including real gases and different types of thermodynamic processes. The discussion highlights the complexity of these concepts without resolving the ambiguities present.

mech-eng
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I have become almost sure but have only some small doubts. Are all isothermal process actually ideal gas equation PV=mRT? If all such processes are occur in closed systems, this is so. Because it is isothermal the temperature is constant, R is constant and so is mass for a closed system. So the left side of the equation should be PV, which is a polytropic process with n=1. But my doubts comes from that in books PV=mRT is always called ideal gas equation, not a polytropic process with n=1 and when it comes to a isothermal process they use ideal gas equation.

Thank you.
 
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mech-eng said:
I have become almost sure but have only some small doubts. Are all isothermal process actually ideal gas equation PV=mRT? If all such processes are occur in closed systems, this is so. Because it is isothermal the temperature is constant, R is constant and so is mass for a closed system. So the left side of the equation should be PV, which is a polytropic process with n=1. But my doubts comes from that in books PV=mRT is always called ideal gas equation, not a polytropic process with n=1 and when it comes to a isothermal process they use ideal gas equation.

Thank you.
Real gases do not exactly obey the ideal gas law. And solids and liquids definitely do not obey the ideal gas law.

Also, in irreversible processes, even though the outer boundary of the gas may be held at constant temperature, the temperature is not constant throughout the body of the gas, and varies with spatial position and time. However, some would regard this as an isothermal process.
 
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Chestermiller said:
Real gases do not exactly obey the ideal gas law. And solids and liquids definitely do not obey the ideal gas law.

Also, in irreversible processes, even though the outer boundary of the gas may be held at constant temperature, the temperature is not constant throughout the body of the gas, and varies with spatial position and time. However, some would regard this as an isothermal process.

What I meant to ask is neither for reals gases, nor if is there any real isothermal process. In this link second question is both related to ideal gas and its being a polytropic process. The second question in the link directly uses ideal gas equation as a polytropic process. So are all polytropic processes actually ideal gas equation?

http://home.iitk.ac.in/~suller/lectures/lec5.htm

Thank you very much.
 
Last edited:
mech-eng said:
What I meant to ask is neither for reals gases, nor if is there any real isothermal process. In this link second question is both related to ideal gas and its being a polytropic process. The second question in the link directly uses ideal gas equation as a polytropic process. So are all polytropic processes actually ideal gas equation?

http://home.iitk.ac.in/~suller/lectures/lec5.htm

Thank you very much.
Sorry. I don't understand your question. In the 2nd problem, they are analyzing the isothermal reversible expansion of an ideal gas. If the question is, "for a constant temperature reversible expansion, is it possible to satisfy an polytropic equation for a real gas, or does it have to be an ideal gas?", I think the answer is that it has to be an ideal gas.
 
Chestermiller said:
Sorry. I don't understand your question. In the 2nd problem, they are analyzing the isothermal reversible expansion of an ideal gas. If the question is, "for a constant temperature reversible expansion, is it possible to satisfy an polytropic equation for a real gas, or does it have to be an ideal gas?", I think the answer is that it has to be an ideal gas.

1. Can there be any polytropic process with the indice equals to 1 which is described by an equation right hand side is not mRT?

2. Can there be any isothermal polytropic process having an indice other than 1?

I hope I am clear enough now.

Thank you.
 
mech-eng said:
1. Can there be any polytropic process with the indice equals to 1 which is described by an equation right hand side is not mRT?

2. Can there be any isothermal polytropic process having an indice other than 1?

I hope I am clear enough now.

Thank you.
In my judgment as an experienced engineer, I see very little value in your spending your valuable time speculating about esoteric things like this. Your time would much better be served getting practice solving thermodynamics problems.
 

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