Intuitive Explanation of Adiabatic Condition

  • Context: High School 
  • Thread starter Thread starter Sudarshan_Hebbar
  • Start date Start date
Click For Summary

Discussion Overview

The discussion revolves around understanding the derivation of the adiabatic condition in thermodynamics, focusing on intuitive explanations and the mathematical framework involved. Participants explore concepts related to ideal gases, conservation of energy, and specific heat, as well as the differential equations that describe these processes.

Discussion Character

  • Exploratory, Technical explanation, Conceptual clarification

Main Points Raised

  • One participant seeks an intuitive understanding of the derivation of the adiabatic condition.
  • Another references the Feynman Lectures as a potentially useful resource for discussions on ideal gases.
  • Several participants inquire about which specific part of the derivation is found to be unintuitive, suggesting it may relate to the laws, definitions, or the mathematical aspects involved.
  • A participant describes the differential equation as relating pressure changes to volume changes in an adiabatic system, emphasizing the connection between internal energy, work done by the gas, and volume change.
  • There is a correction regarding the equation for the change in the product of pressure and volume, with one participant asserting that the correct form involves differentials rather than finite changes.
  • Another participant reiterates the focus on the differential equation and its relation to pressure and volume changes in the context of an adiabatic process.

Areas of Agreement / Disagreement

Participants express varying levels of understanding regarding the derivation, with some seeking clarification on specific components. There is no consensus on which aspects are most challenging or how to best intuitively connect the concepts.

Contextual Notes

Some participants mention the need for clarity on the differential equation and its implications, indicating potential gaps in understanding the mathematical relationships involved in the adiabatic process.

Sudarshan_Hebbar
Messages
17
Reaction score
4
IMG_0024.webp

How to understand this derivation in a very intuitive way?
 
Last edited by a moderator:
Science news on Phys.org
As I recall the Feynman Lectures have some usefull discussions for ideal gas.
 
Reply
  • Like
Likes   Reactions: Sudarshan_Hebbar
Which part are you finding unintuitive?

It is basically the conservation of energy, the ideal gas law, the definitions of specific heat, and a bunch of math. So is it the laws, the definitions, or the math?
 
Dale said:
Which part are you finding unintuitive?

It is basically the conservation of energy, the ideal gas law, the definitions of specific heat, and a bunch of math. So is it the laws, the definitions, or the math?
Mainly, The differential equation. I imagine that it Is describing the process of a small volume change in an adiabatic system and how the pressure is changing in accordance with

1. the increase in internal energy due to work done by the gas.
2. The change in Volume.

How can I connect these two outcomes to the diffential equation?
 
Sudarshan_Hebbar said:
View attachment 363379
How to understand this derivation in a very intuitive way?
The equation ##\Delta (PV)=P\Delta V+V\Delta P## is incorrect. It should read d(PV)=PdV+VdP. $$\Delta (PV)=P_2V_2-P_1V_1=\left(\frac{P_1+P_2}{2}\right)\Delta V+\left(\frac{V_1+V_2}{2}\right)\Delta P$$
 
Reply
  • Like
Likes   Reactions: TensorCalculus and Sudarshan_Hebbar
Sudarshan_Hebbar said:
Mainly, The differential equation.

It's relates dP to dV.

Sudarshan_Hebbar said:
I imagine that it Is describing the process of a small volume change in an adiabatic system and how the pressure is changing

I would just end that sentence there.
 

Similar threads

High School Adiabatic processes and temperatures
  • · Replies 2 ·
Replies
2
Views
2K
High School Comparing energy released to the energy needed to compress a gas (game design scenario)
  • · Replies 14 ·
Replies
14
Views
2K
Undergrad Irreversible adiabatic processes & entropy change (clarification needed)
  • · Replies 22 ·
Replies
22
Views
6K
Intuitive explanation of Fanno Flow
  • · Replies 2 ·
Replies
2
Views
3K
Undergrad Identification of changes in internal energy with work (in Callen's Thermodynamics)
  • · Replies 5 ·
Replies
5
Views
1K
High School Understanding Laplace's Correction and the Adiabatic Process
  • · Replies 2 ·
Replies
2
Views
1K
Undergrad Is there a bad intuition or bad explanation in quantum entanglement?
  • · Replies 48 ·
2
Replies
48
Views
3K
Undergrad Description of Adiabatic Expansion
  • · Replies 8 ·
Replies
8
Views
2K
Undergrad Confusion between adiabatic and energy
  • · Replies 20 ·
Replies
20
Views
4K
High School Heat exchange after thermal equilibrium
  • · Replies 2 ·
Replies
2
Views
2K