# Maximum Work Theorem : Herbert Callen

• mayank pathak
In summary, the conversation discusses the concept of reversible heat sources and their role in thermodynamics, specifically in relation to the fundamental equation of the heat source. The speaker shares their understanding of the concept and raises a question about the necessity of a reversible heat source. They also mention their difficulty in understanding the topic and suggest another textbook as a potential resource.
mayank pathak
Hi, I have been studying thermodynamics from Herbert Callen's "Thermodynamics : an introduction to the physical theories of equilibrium thermostatics and irreversible thermodynamics"
In Chapter 4, Section 4.4, he writes : "
all processes occurring between a given initial and a given final state of a system, the flux of heat to an associated reversible heat source is minimum and the flux of work to an associated reversible work source is maximum for reversible processes."

Now he also describes what a reversible heat source is : "
A reversible heat source is defined as a system enclosed by a rigid
impermeable wall and characterized by relaxation times sufficiently short
that all processes of interest within it are essentially quasi-static."

I understand his argument. But I fail to understand why is the heat source required to be reversible ? According to me, as long as the heat source(or sink) is constrained to have constant volume and constant mole numbers, same heat input will lead to same rise in internal energy and hence same increase in entropy in accordance with the fundamental equation of the heat source. And that is all that we need to prove maximum work theorem. And we don't actually need the heat source to be reversible.

Am I missing something ?

Edit : I have uploaded the relevant text from the book.

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For what it is worth, none of it makes any sense to me.

Chestermiller said:
For what it is worth, none of it makes any sense to me.

does my question sound incomplete ? Let me share some pages from the book to make it easy for others.

None of it makes any sense to me. It is well known that, for two specified thermodynamic equilibrium states of a closed system, there are an infinite number of reversible paths, and they don't all involve the same work and heat.

As an alternate to Callen, might I suggest Fundamentals of Engineering Thermodynamics by Moran et al. I think you will find it much easier to understand.

## What is the Maximum Work Theorem proposed by Herbert Callen?

The Maximum Work Theorem, also known as the Maximum Work Principle, is a thermodynamic principle proposed by Herbert Callen. It states that in a thermodynamic system, the maximum amount of work that can be extracted is equal to the change in Helmholtz free energy.

## How is the Maximum Work Theorem applied in thermodynamic systems?

The Maximum Work Theorem is applied by considering a reversible process, where the system is in equilibrium at all times. This allows for the maximum amount of work to be extracted from the system.

## What is the significance of the Maximum Work Theorem in thermodynamics?

The Maximum Work Theorem is significant as it provides a way to determine the maximum amount of work that can be obtained from a thermodynamic system. This knowledge can be used in practical applications, such as designing efficient engines.

## Are there any limitations to the Maximum Work Theorem?

Yes, the Maximum Work Theorem is limited to reversible processes and assumes that the system is in equilibrium at all times. In real-world scenarios, irreversible processes and non-equilibrium conditions may occur, making the application of this theorem difficult.

## Have there been any criticisms of the Maximum Work Theorem proposed by Herbert Callen?

Yes, there have been criticisms of the Maximum Work Theorem, particularly in regards to its practical application. Some argue that it is difficult to determine the maximum work that can be extracted in real-world scenarios, as it requires precise control and measurement. Others also argue that it may not hold true for all thermodynamic systems.

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