About Reversible vs Irreversible Gas Compression and Expansion Work

[cianfa72]

Hi,

reading the interesting Reversible vs Irreversible Gas Compression and Expansion Work insight by @Chestermiller I would like to ask for clarification on some points.

In the second bullet at the beginning

Since, by Newton’s third law, the external force per unit area exerted by the surroundings on the gas is equal to the gas thermodynamic pressure at the interface P.

my understanding is as follows: consider an ideal gas contained in a cylinder featuring a massless piston. An external force per unit area $P_{ext}$ is applied to the piston through a bunch of (external) bodies.

Applying the Newton's third laws to the massless piston we get two things:

• the force per unit area the piston applies to the external bodies through the piston's outer edge is the same (in module) as the external force per unit area $P_{ext}$
• the force per unit area the thermodynamic pressure of the gas at the piston's inner edge $P_I$ (i.e. the thermodynamic pressure $P_I$ at the piston internal interface) applies to the piston is the same (in module) as the force the piston applies per unit area on the gas inside the cylinder

The above hold since otherwise the acceleration of the massless piston would be infinite.

Does it make sense ? Thank you.

 

[Chestermiller]

Hi,

reading the interesting Reversible vs Irreversible Gas Compression and Expansion Work insight by @Chestermiller I would like to ask for clarification on some points.

In the second bullet at the beginning

my understanding is as follows: consider an ideal gas contained in a cylinder featuring a massless piston. An external force per unit area $P_{ext}$ is applied to the piston through a bunch of (external) bodies.

Applying the Newton's third laws to the massless piston we get two things:

• the force per unit area the piston applies to the external bodies through the piston's outer edge is the same (in module) as the external force per unit area $P_{ext}$
• the force per unit area the thermodynamic pressure of the gas at the piston's inner edge $P_I$ (i.e. the thermodynamic pressure $P_I$ at the piston internal interface) applies to the piston is the same (in module) as the force the piston applies per unit area on the gas inside the cylinder

The above hold since otherwise the acceleration of the massless piston would be infinite.

Does it make sense ? Thank you.

Yes it does make sense. But, in the way that I define things, I would consider $P_{ext}$ to be the force per unit area that the inside face of the piston applies to the gas. Otherwise, based on the way you have defined $P_{ext}$, I would have to include the piston as part of the system. Of course, in this situation it doesn't matter, but, if the piston had mass and thermal inertia, by my way of doing things, the piston would have to be included as part of the system.

Also, I should mention that, if the process is irreversible, the force per unit area applied by the gas to the inside face of the piston would conceptually have to include the viscous normal stress.

 

[cianfa72]

Yes it does make sense. But, in the way that I define things, I would consider $P_{ext}$ to be the force per unit area that the inside face of the piston applies to the gas. Otherwise, based on the way you have defined $P_{ext}$, I would have to include the piston as part of the system. Of course, in this situation it doesn't matter, but, if the piston had mass and thermal inertia, by my way of doing things, the piston would have to be included as part of the system.

Yes, definitely.

Also, I should mention that, if the process is irreversible, the force per unit area applied by the gas to the inside face of the piston would conceptually have to include the viscous normal stress.

Of course, as you explained in the 'Spring-Damper Model Analysis' and 'Ideal Gas Analysis' sections.

 

[Chestermiller]

Yes, definitely.Of course, as you explained in the 'Spring-Damper Model Analysis' and 'Ideal Gas Analysis' sections.

You are wonderful. I hope that you continue to stay involved with Physics Forums. It's so nice to encounter someone like you who is on the same wavelength as I.

 

[cianfa72]

By the way: in the insight I do not see 'Figure 8 Work Done By Viscous Stresses on Piston' and the sentence

Fig. 9 shows a plot of the ratio of the irreversible work to the reversible work $W_{Irr} / W_R$ for the case of an ideal gas as a function of the expansion/compression volume ratio $W_f / W_i$

should actually read:

Fig. 9 shows a plot of the ratio of the irreversible work to the reversible work $W_{Irr} / W_R$ for the case of an ideal gas as a function of the expansion/compression volume ratio $V_f / V_i$