Why is PV work in thermodynamics so difficult to understand?

[Est120]

Homework Statement

Expression for "Work" in thermodynamics

Relevant Equations

Newton's 2nd law, ideal gas equation of state

i can't manage to grasp the concept of PV work in thermodynamics, for example we all know that W= integral(F*dx) like here

but this says that, at the end, W doesn't really depend on the gas temperature or reversible process crap
at the end W is simply a constant, atmospheric pressure is constant, piston weight is constant (and since V2=V1=0, and we neglect friction)
so that's absolutely understandable for me but in thermodynamics books:

and this doesn't agree with the first equation because here we need to have a reversible process in such a way that we can always associate a definite value for P to the gas
there is absolutely NO book that explains PV work in an understandable way , in thermodynamics work isn't just "Force x distance"

 

[Chestermiller]

This assumes that you don't know how to calculate the force exerted by the gas in an irreversible process. However, you can use the other forces acting on the piston to determine what the work is that the gas does. Do you think that, in an irreversible expansion or compression, an ideal gas satisfies the ideal gas law?

 

[Est120]

then why do we need all the reversible path crap also the value for W according to the "normal" formula (F*dist) at the end is always the same regardless of the path (mg and Pa are always the same in te process)
using that formula you can't differentiate from an isothermal or adiabatic or x process.
there are some things in thermodynamics that i will assume i will never understand

 

[Chestermiller]

The work is not always the same. This is a specific case in which you know the external force but may not necessarily directly know the force of the gas. So the formula still enables you to calculate the work.

The thing to remember is that, by Newton's 3rd law, the force per unit area exerted by the gas on the piston is always equal in magnitude and opposite in direction to the force per unit area exerted by the piston on the gas. However, the ideal gas law only applies to thermodynamic equilibrium states of the gas (and to reversible processes, which all consist of a continuous sequence of thermodynamic equilibrium states). So, for an irreversible process, you can't get the force per unit area exerted by the gas on the piston using the ideal gas law (or other equation of state). You need to hope that you can determine the work indirectly using the external forces. Sometimes, you can do that, but many times you can't. In the example they gave, where the external pressure and the friction force are known, you can determine the work ( at least in the end where the piston kinetic energy has been dissipated).

In terms of differentiating processes, you can always identify an adiabatic process because, in such a process, the cylinder is insulated and there is no heat transferred to or from the gas.

If the process is irreversible, the temperature of the gas may not be uniform spatially within the cylinder, so saying that it is isothermal is problematic. Some people regard an irreversible isothermal process as one in which the cylinder is held in contact with a constant temperature reservoir throughout the process, at the same temperature as the initial temperature of the gas. This certainly allows heat transfer to occur to the gas, so that the process is not adiabatic. But, during this irreversible change, the temperature of the gas inside the cylinder is not uniform at the reservoir temperature.

Be aware that, in an irreversible process, the gas pressure depends not only on the gas volume but also on the time rate of change of gas volume. So it is a rate process.

The reason that you have so much trouble understanding thermodynamics is not your fault. It's just that most of the textbooks out there are so poorly written.