B Intuitive Explanation of Adiabatic Condition

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Understanding the derivation of the ideal gas behavior involves concepts like conservation of energy, the ideal gas law, specific heat definitions, and differential equations. The discussion highlights confusion around the differential equation that describes pressure changes during small volume changes in an adiabatic system. The correct formulation of the equation is crucial, as it connects changes in pressure and volume. The participants seek a more intuitive grasp of how these elements interrelate, particularly in the context of the ideal gas behavior. Clarity on these mathematical relationships is essential for a deeper understanding.
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How to understand this derivation in a very intuitive way?
 
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As I recall the Feynman Lectures have some usefull discussions for ideal gas.
 
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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:
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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. $$\Delta (PV)=P_2V_2-P_1V_1=\left(\frac{P_1+P_2}{2}\right)\Delta V+\left(\frac{V_1+V_2}{2}\right)\Delta P$$
 
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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.
 

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