Adiabatic Process (Poisson’s equations)

[Taulant Sholla]

Homework Statement

I'm lacking clarity with the statements I highlighted in the passage found in my physics textbook. It is stated that P, V, and T all vary during an adiabatic process, but the next box I highlighted uses dW=PdV which assumes pressure is constant during this process. These seem to be contradictory statements. What am I missing here? Thank you.

Relevant Equations

dW=PdV

 

[TSny]

the next box I highlighted uses dW=PdV which assumes pressure is constant during this process.

The relation $dW = PdV$ does not assume that $P$ is constant during the process.

A similar example would be a particle moving along the x-axis with a varying velocity. At some instant of time, you can write the instantaneous velocity as $v = dx/dt$. This can be "rearranged" as $dx = vdt$. So, the displacement during an infinitesimal time interval $dt$ is $dx = vdt$. This is valid even though $v$ is not constant during the motion.

 

[Lnewqban]

Please, look for "Derivation of P–V relation for adiabatic heating and cooling" at this article:
https://en.wikipedia.org/wiki/Adiabatic_process

 

[Taulant Sholla]

The relation $dW = PdV$ does not assume that $P$ is constant during the process.

A similar example would be a particle moving along the x-axis with a varying velocity. At some instant of time, you can write the instantaneous velocity as $v = dx/dt$. This can be "rearranged" as $dx = vdt$. So, the displacement during an infinitesimal time interval $dt$ is $dx = vdt$. This is valid even though $v$ is not constant during the motion.

Please accept my belated thank you! This really helped!

 

[Taulant Sholla]

Please, look for "Derivation of P–V relation for adiabatic heating and cooling" at this article:
https://en.wikipedia.org/wiki/Adiabatic_process

I did, it didn't help. Thanks anyway - I got an assist from another kind soul.