# Principles for Understanding Heat Treating Materials: Thermodynamics (Part 2)

by Mike Powers, F.A.S.M.

In part 1 of this article we explored the definition of a thermodynamic system, the transfer of matter and energy across system boundaries, what is meant by system equilibrium, the definition of state functions, and the modes of energy transfer as expressed by work and heat. In part 2 we will investigate the Laws of Thermodynamics and their implications for process spontaneity, process irreversibility and the importance of the Gibbs free energy.

For our purposes, we will focus on the 1^{st} and 2^{nd} Laws of Thermodynamics (i.e. we will forgo a discussion of the 3^{rd} Law). However, to establish the 1^{st} Law we need to first discuss the Zeroth Law.

**The Zeroth Law Does Truly Exist**

The Zeroth Law is not an original law; it was established after 1^{st} and 2^{nd} Laws, around 1935 by Ralph Fowler and Edward Guggenheim. The 0^{th} Law states that two bodies, each in thermal equilibrium with a third body, are in thermal equilibrium with each other. You may be thinking, “So what?” Well, this law establishes that the bodies have a property in common, which can be measured. This property is temperature. In other words, temperature is the “degree of hotness” of a body relative to another. A body that “feels hotter” than an adjacent body has a higher temperature. Basically, the 0^{th} Law establishes the concept of temperature.

**Let’s Talk About the 1 ^{st} Law of Thermodynamics**

When talking about the 1^{st} Law of Thermodynamics, we consider a system at state A which performs work and absorbs heat and moves to state B. Heat that is absorbed by the system increases the internal energy of the system by amount “q.” The work done by the system decreases the internal energy of the system by amount “w.” So the change in the internal energy of the system can be defined as:

**Δ****U = U _{B} – U_{A} = q – w.**

That’s it, the 1^{st} Law. The 1^{st} Law establishes the definition of internal energy, the equivalence of work and heat and the concept that the internal energy of a system is a function only of the state of the system and not the means by which the system arrived at the given state. Internal energy is a state function.

The cool thing about the 1^{st} Law (pun intended) is that it owes to the work of James Joule in the 1840s while he was working in his father’s brewery. Between sips of brew no doubt, Joule conducted experiments in which work was performed in a quantity of adiabatically contained water (i.e. prohibit or minimize the passage of heat between the system and surroundings) and measured the resultant temperature rise of the water. Examples include rotating a paddle wheel immersed in the water, an electric motor driving a current through a coil immersed in the water, compressing a cylinder of gas immersed in the water and rubbing together two metal blocks immersed in the water. He observed that a direct proportionality existed between the work done and the resultant temperature rise, no matter what means were employed in the production of the work.

**Interpreting the 1 ^{st} Law **

Besides the definition of internal energy described by the equation above, the 1^{st} Law can be expressed in words in a variety of ways.

- The increase in internal energy of a closed system is equal to the difference of the heat supplied to the system and work done by it
- The total energy of an isolated system can’t change (i.e. energy is conserved)
- Energy can’t be created or destroyed, it can only change form
- You can’t get more energy out of a system than you put into it

In theoretical thermodynamics, a reversible process is one in which the system changes in such a way that the system and its surroundings can be put back in their original states by exactly reversing the process path, without any dissipation of energy, because all along the process path the system is in thermodynamic equilibrium. However, since it takes an infinite amount of time for a truly reversible process to finish, perfectly reversible processes are impossible (i.e. reversible processes are a theoretical construct). By contrast, an irreversible process is one where changes in the system can’t be undone by exactly reversing the change to the system. So, even if the system is returned to its original condition, the surroundings would have changed. Finally, a spontaneous process is one that proceeds on its own without any outside intervention. Processes that are spontaneous in one direction are not spontaneous in the reverse direction. Examples include the rusting of a nail, the explosion of metallic Na when placed in water, or the melting of ice/freezing of water.

Enthalpy is a thermodynamic quantity equal to the internal energy of a system plus the product of its volume and the pressure exerted on it by its surroundings, or H = U + PV. Since U (internal energy), P (pressure) and V (volume) are functions of state, so is H, the enthalpy. For a process at constant pressure, the change in enthalpy is simply the heat admitted to or withdrawn from the system: ΔH = H_{B} – H_{A} = q_{p}. The S.I. unit of measurement for enthalpy is (you guessed it) the joule. If ΔH > 0, the process is exothermic because energy is released by the system to the surroundings. If ΔH < 0, the process is endothermic because energy is absorbed by the system from its surroundings.

**Cruising Through the 2 ^{nd} Law of Thermodynamics**

In 1854, Rudolph Clausius defined the ratio of the heat delivered to an ideal engine and the constant temperature at with the heat is delivered as the entropy,

Like the internal energy (U) and the enthalpy (H), the entropy (S) is a state function. Based on an ideally reversible cycle, he showed that the incremental change in entropy is,

This then is the mathematical expression for the 2^{nd} Law of Thermodynamics. Now for an isolated system,

**dS ****≥**** 0.**

So the incremental change in entropy for a reversible process is zero and positive for an irreversible process. Since there is no such thing as a thermodynamically reversible process and since the universe (system + surroundings) constitutes an isolated system, the entropy for any process must be greater than zero and the entropy of the universe is positive. The 2^{nd} Law can be variously expressed in words.

- The entropy of an isolated system never decreases
- Complete conversion of heat into work is not possible without causing some effect elsewhere
- The sum of the entropy change of the system and surroundings for any spontaneous process is always greater than zero
- The entropy of the universe increases

**Expressions of the 2 ^{nd} Law is Like Music to Our Ears**

You probably didn’t realize that Keith Richards and Mick Jaeger of the Rolling Stones are closet thermodynamicists. They even wrote a song about the 2^{nd} Law, which I’m sure you have heard, called, ”You Can’t Always Get What You Want.” OK, I made that up, but I trust you get the point.

Our hero J. Willard Gibbs proposed a new state function in 1873, now named the Gibbs free energy (G), which he defined as G = H – TS. G defines the ability of the system to do work at constant temperature (T) and pressure (P), so that the system does only volume (V) work. The change in Gibbs free energy is mathematically expressed as,

**Δ****G = ****Δ****H – T****ΔS.**

The ramifications of this astute principle are huge. For a closed system that is only able to perform volume work on its surroundings (i.e. constant T and P), the Gibbs free energy can remain unchanged or it can decrease, but it can never increase,

**Δ****G _{T,P} **

**≤**

**0.**

As such, for a system at equilibrium under constant temperature and pressure **Δ****G _{T,P} **

**=**

**0.**Wow, now we have a precise definition of system equilibrium under the conditions of constant T and P. So, for a particular change of state at constant T and P, if the change in Gibbs free energy is less than zero, the process is possible and will occur. If the value of ΔG is greater than zero then the process is not possible and will not occur and if ΔG is precisely zero then the initial and final states of the system are in equilibrium. It also means that if the change in Gibbs free energy is negative, the process is spontaneous. This is heady stuff because we now realize that a closed system will drive toward equilibrium in order to minimize the value of ΔG consistent with the fixed values of temperature and pressure. The change in Gibbs free energy is the driving force for changes of state in closed systems at constant temperature and pressure, including chemical reactions. We will see in subsequent articles how truly important this concept is and how it can be applied to practical applications.

Copyright © 2017 by Michael T. Powers – All rights reserved.