Change in Internal Energy of an Isobaric Process

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Discussion Overview

The discussion revolves around the change in internal energy of a monatomic ideal gas during an isobaric process, specifically addressing the discrepancies in calculations of work done and internal energy change. Participants explore the implications of the ideal gas law and the definitions of internal energy in different contexts.

Discussion Character

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

Main Points Raised

  • One participant notes that in an isobaric expansion, the work done by the gas calculated as pressure times change in volume yields 5000J, while using the ideal gas law gives a change in internal energy of 415.5J, leading to confusion about the fundamental concepts involved.
  • Another participant questions the value of ΔT used in the calculations, prompting a clarification that ΔT is 50K.
  • A participant reflects on confusion stemming from mixing concepts of internal energy changes for different materials and ideal gases, indicating a struggle with the theoretical framework.
  • Further clarification is provided that the temperature change must be determined by the parameters of the process, with an example calculation showing that ΔT could actually be 1203K, leading to a work calculation of 10,000J.
  • Another participant prompts a deeper inquiry into the relationship between work, heat added, and internal energy change, referencing the equation ΔU = Q - PΔV and asking for clarification on the implications of these relationships.

Areas of Agreement / Disagreement

Participants express varying levels of understanding and confusion regarding the calculations and concepts involved. There is no consensus on the correct interpretation of the results or the underlying principles, indicating ongoing debate and exploration of the topic.

Contextual Notes

Participants highlight potential limitations in their understanding, particularly regarding the definitions and applications of internal energy in different contexts, as well as the assumptions made in calculations related to temperature changes and work done.

Who May Find This Useful

This discussion may be useful for students and individuals studying thermodynamics, particularly those grappling with concepts related to ideal gases, internal energy, and isobaric processes.

jeff.berhow
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In an isobaric process of 1 mole of a monatomic ideal gas, the pressure stays the same while the volume and temperature change. Let's take an isobaric expansion where the volume increases by 2m3 and the pressure stays at 5kPa.

If the work done by the gas is the pressure times the change in volume we get 5000J, but if we apply the ideal gas law to that equation, we get nRΔT, which then gives an amount of 415.5J. In the first instance, the change in internal energy decreases which is weird to me. In the second, it acts accordingly and increases.

What is the fundamental issue I am having dealing with this concept, and why do we effectively learn two ways of calculating gas processes?

Thanks in advance. For some reason, Thermodynamics is kicking my butt because I can't conceptualize it correctly.
 
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How do you get that second result? What is your ΔT?
 
Ah, sorry, let's say the delta T is 50K.
 
I think I'm starting to understand what I'm getting confused on. Our first chapter discussed change in internal energy in the context of any type of material, and the second chapter discusses ideal gases and their change in internal energy. I think I am getting the two mixed up and mixing and matching them. This is very disheartening.
 
jeff.berhow said:
Ah, sorry, let's say the delta T is 50K.

You cannot just "say" it. It's not arbitrary but determined by the given parameters and process.
You could "say" that the initial temperature is 50 K (for instance). This will give you an initial volume
V1=nRT1/P = 0.0831 m^3
Then V2 should be 2.0831 m^3 and the final temperature
T2=pV2/nR=1253 K.
So ΔT = 1203 K.
With this you will get the same work if you use nRΔT as by using p ΔV directly.
Work which, by the way, is 10,000J and not 5000J.

The nice thing is that no matter what T1 is, the things will "arrange" such that the work will be same, for the given parameters.
 
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Let me guess. You are trying to calculate the temperature change and the heat added Q. If PΔV=10000 J, from the ideal gas law what is nRΔT equal to? If you have n = 1 mole, what is the temperature change? What is the equation for the change in internal energy ΔU of a monotonic ideal gas in terms of n, R, and ΔT? From this equation, what is change in internal equal to? The ideal gas law tells you that ΔU=Q-PΔV? Using this equation and the results so far, what is Q equal to?
 

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