Fundamentals of Thermodynamics

John H. S. Lee, K. Ramamurthi

• Publisher: CRC Press
• Year: 2022
• ISBN:
  9781000533200
• Edition: 1
• Topic: Physical Sciences
• Subtopic: Energy

A concise treatment of the fundamentals of thermodynamics is presented in this book. In particular, emphasis is placed on discussions of the second law, a unique feature of thermodynamics, which states the limitations of converting thermal energy into mechanical energy. The entropy function that permits the loss in the potential of a real thermodynamic process to be assessed, the maximum possible work in a process, and irreversibility and equilibrium are deduced from the law through physical and intuitive considerations. They are applicable in mitigating waste heat and are useful for solving energy, power, propulsion and climate-related issues.

The treatment is not restricted to properties and functions of ideal gases. The ideal gas assumption is invoked as a limiting case. Reversible paths between equilibrium states are obtained using reversible heat engines and reversible heat pumps between environment and systems to determine the entropy changes and the maximum work. The conditions of thermodynamic equilibrium comprising mechanical, thermal, chemical and phase equilibrium are addressed and the species formed at equilibrium in a chemical reaction at a given temperature and pressure are obtained. The molecular basis for the laws of thermodynamics, temperature, internal energy changes, entropy, reversibility and equilibrium are briefly discussed.

The book serves as a reference for undergraduate and graduate students alongside thermodynamics textbooks.

1 Fundamental Concepts

DOI: 10.1201/9781003224044-1

1.1 System and Environment

Thermodynamics is a study of the interaction of a system with its environment. A system is part of the universe contained within a prescribed boundary that we deal with. Everything outside the boundary is called the environment. Thus, the system and its environment constitute the universe.

The boundary of a system may be a real physical boundary or could be imaginary. The boundary may be of arbitrary shape and could move when the volume within the boundary changes such as when the system expands or contracts when interacting with the environment.

An isolated system has a boundary that does not permit mass or energy exchange across it. For a closed system, the boundary permits only energy exchange. If mass as well as energy is exchanged across the boundary, the system is called an open system.

1.2 State of a System

The state of a system is defined by a set of measurable macroscopic parameters. The state can be measured only if the variables defining the state are invariant with respect to time and space within the system; that is, the system is in equilibrium. It is the equilibrium state of a system that is defined by the state variables of a system.

State variables that depend on the mass of the system are called extensive variables, for example, energy and volume. State variables that are independent of the mass are called intensive variables, for example, pressure, density and temperature. The specific value of an extensive property is the extensive property divided by the amount of substance, for example, specific volume $v=\frac{V}{m}$, where V is the volume and m is the mass.

1.3 Simple Systems

We shall be dealing mostly with simple systems. A simple system is one which is homogeneous, isotropic and chemically inert. It is sufficiently large in that surface effects can be neglected. In other words, we may define its energy without considering the surface energy due to the boundary separating the system from the environment. The external forces arising from electromagnetic, gravitational and similar environmental effects are also not considered in contributing to the energy of the simple system. So the simple system can generally be defined solely by its energy U, volume V and amount of mass in the system, that is, (U, V, m_i) where m_i is the mass of the different chemical components “i” in the system.

1.4 Mass, Molecular Mass and Moles in a System

The mass of a system is the number of molecules N contained in the system multiplied by the mass of each of the molecules in it. Since the mass of a molecule is very small, it is measured in terms of the mass of a standard particle that is chosen to have a mass one-twelfth the mass of an isotope of carbon $\stackrel{12}{C}$. The mass of the standard particle $m_0$, known as the atomic mass unit (a.m.u.), is 1.661×10⁻²⁴ g.

The mass of a molecule of a substance is therefore expressed in units of the standard atomic mass unit m₀, namely, mass of the molecule m divided by $m_0$_, that is, $M=\frac{m}{m_0}$. M is called the molecular mass.

As an example, the molecular mass of a hydrogen molecule is given as $M_{H_2}=\frac{m_{H_2}}{m_0}$_, where $m_{H_2}$ is the mass of the hydrogen molecule and $m_0$ is the mass of the standard particle. It is also spoken of as molecular weight since almost all experiments are carried out in the vicinity of the Earth’s surface where the gravitational constant is the same. We will use the words molecular mass and molecular weight without differentiating between them.

The number of molecules in a macroscopic system is, in general, very large, and we therefore measure it in the unit of mole. A mole is defined as the number of standard particles N₀ in 1 g of it, that is, $N_0=\frac{1}{m_0}=\frac{1}{1.661\times {10}^{-24}}=6.023\times {10}^{23}$_, N₀ is called Avogadro number.

The number of the moles of a substance comprising of N molecules is $n=\frac{N}{N_0}$.

We can write the molecular mass as

$$M=\frac{m}{m_0}=\frac{m}{m_0}\frac{N_0}{N_0}=m{N}_0$$(1.1)

since $m_0{N}_0$ = 1 g.

The molecular mass M therefore equals mN₀ in unit of grams and is the mass of 1 mole of the substance in grams. Thus, 1 mole of hydrogen has a mass equal to 2 g, and 1 mole of nitrogen is 28 g and so on. Similarly, the number of moles n of a substance of mass m g is m/M.

For a mixture of gases consisting of N different constituents, the mole fraction of the ith constituent in it is

$$x_i=\frac{n_i}{{\displaystyle \sum _{i=1}^{i=N}{n}_i}}$$

where $n_i$ mole is the number of moles of the ith constituent in it and ${\displaystyle \sum _{i=1}^{i=N}{n}_i}$ is the total number of moles in the mixture.

Similarly, if the mass of the ith constituent is m_i, the mass concentration of the ith constituent is

$$y_i=\frac{m_i}{{\displaystyle \sum _{i=1}^{i=N}{m}_i}}$$

The sum of the mole fractions and mass fractions is unity, namely,

$${\displaystyle {\sum }_{i=1}^N{x}_i=1},{\displaystyle {\sum }_{i=1}^N{y}_i=1}$$

1.5 Intensive Variables Defining a System

Energy U, volume V and mass m or equivalently the moles n, which define a system, are based on the extent of a system. The energy per unit mass $u=\frac{U}{m}$ and the specific volume $v=\frac{V}{m}$ are independent of the extent and are intensive variables. In the following, we define the intensive variables pressure and temperature for defining a simple system. These are independent of its extent and are the so-called intensive variables.

1.5.1 Pressure

The pressure p is the force per unit area and act...