B Intuitive Explanation of Adiabatic Condition

[Sudarshan_Hebbar]

How to understand this derivation in a very intuitive way?

 

[hutchphd]

As I recall the Feynman Lectures have some usefull discussions for ideal gas.

 

[Dale]

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?

 

[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?

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?

 

[Chestermiller]

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. $$\Delta (PV)=P_2V_2-P_1V_1=\left(\frac{P_1+P_2}{2}\right)\Delta V+\left(\frac{V_1+V_2}{2}\right)\Delta P$$

 

[Herman Trivilino]

Mainly, The differential equation.

It's relates dP to dV.

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.