Statistical Mechanical interpretation of work and heat

[Andrew_]

According to my thermal physics book , from classical thermodynamics for a reversible change :

$$dU = dQ - dW$$

From stat mech ,

$$dU = \sum_i \epsilon _i dn_i + \sum_i n_i d \epsilon _i$$

Then by drawing some arguments from quantum mechanics the writer relates the change in volume and therefore work to the change in the energy levels. ( although there are more general treatments that include electric/magnetic fields ... )
The populations , ni , however, are unaltered. Only by supplying heat to the system do the populations change and therefore will there be entropy change to the system ofcourse without altering the energy levels.

But what if the process were irreversible ? For an adiabatic irreversible change dQ =0 , so dS > 0 , and therefore I can safely conclude that the separation of dW and dQ terms cannot be done here. That is , the usual interpretation of work and heat is just wrong for any irreversible change.

Is this correct ?

Thanks,

 

[Aaron Barnard]

Yes, this is correct. In an irreversible change, the usual interpretation of work and heat is not applicable, because the energy is not conserved. In an irreversible change, the energy is converted from one form to another, and the amount of energy converted cannot be determined from just the work and heat terms.

 

[astrokreng]

I would like to address the content and provide my response to the interpretation of work and heat in the context of statistical mechanics.

Firstly, it is important to note that both classical thermodynamics and statistical mechanics are valid approaches to understanding the behavior of thermodynamic systems. While classical thermodynamics is based on macroscopic observations and principles, statistical mechanics provides a microscopic understanding of thermodynamic phenomena.

The equation dU = dQ - dW is a fundamental equation in classical thermodynamics, where dU represents the change in internal energy, dQ represents the heat transferred to the system, and dW represents the work done by the system. This equation holds true for reversible processes, where the system can be brought back to its initial state without any change in the surroundings.

On the other hand, the equation dU = Σiεi dni + Σi ni dεi represents the change in internal energy in terms of the energy levels and their populations, as described by statistical mechanics. This approach considers the microscopic behavior of particles in a system and their interactions.

It is true that for an adiabatic irreversible process, where no heat is exchanged with the surroundings, the change in entropy (dS) is greater than zero. This is because irreversible processes lead to an increase in disorder or randomness in the system, resulting in an increase in entropy. In this case, the traditional separation of work and heat terms cannot be done, as the system is not in equilibrium and the concept of heat transfer is not well-defined.

However, this does not mean that the interpretation of work and heat in classical thermodynamics is incorrect. It simply means that the classical thermodynamic approach is not applicable to irreversible processes. In such cases, statistical mechanics provides a more accurate description of the behavior of the system.

In conclusion, both classical thermodynamics and statistical mechanics are valid approaches to understanding the behavior of thermodynamic systems. While classical thermodynamics is applicable to reversible processes, statistical mechanics provides a better understanding of irreversible processes. It is important to choose the appropriate approach depending on the nature of the process being studied.