Introduction of Thermodynamics and Basic Terminalogies

The term "thermodynamics" originates from two distinct words: "thermo," referring to heat, and "dynamics," which denotes movement. Consequently, "thermodynamics" encapsulates the study of heat flow. In the realm of physical chemistry, this field delves into the quantitative relationships between heat and other forms of energy, occasionally referred to as "energetics." At its core, thermodynamics rests upon four fundamental laws, forming the basis for understanding energy relationships in both physical and chemical processes. These laws facilitate predictions regarding:

1) The likelihood of a chemical reaction occurring upon mixing chemical substances.

2) The amount of energy theoretically required or released during the reaction.

3) The equilibrium extent of a chemical reaction, indicating the ratio of products to reactants.

Chemical thermodynamics primarily concerns itself with the equilibrium position of a reaction, although it does not directly forecast the rate of reaction.

These four laws are:

The Zeroth Law: It establishes the concept of temperature, asserting that if two systems are each in thermal equilibrium with a third system, they are in thermal equilibrium with each other.

The First Law: Also known as the principle of the conservation of energy, it states that energy cannot be created or destroyed in an isolated system, but can only change forms, maintaining the total energy of a closed system.

The Second Law: This law dictates that the total entropy (a measure of disorder or randomness) of an isolated system always increases over time, with any reversible process accompanied by an increase in total entropy. It emphasizes the tendency of natural processes to move towards greater disorder.

The Third Law: It posits that as the temperature of a system approaches absolute zero, the entropy of the system approaches a minimum or constant value, making it impossible to reach absolute zero through a finite number of processes.

These laws, although not derived from experimental data, have undergone rigorous mathematical treatments, correlating with various observable properties of matter across natural phenomena.

Classical thermodynamics concerns itself with the bulk or macroscopic properties of a system, independent of its atomic and molecular structure. Conversely, statistical thermodynamics applies the laws of mechanics to individual molecules, utilizing statistical averages to derive results. The insights gained from classical and statistical thermodynamics complement each other.

The zeroth law introduces the concept of temperature, while the first law emphasizes the equivalence between different forms of energy without specifying the conditions under which such equivalence is achieved. The second law imposes restrictions on the first law and deals with the directions of physico-chemical transformations and the equilibrium properties of the system. The third law focuses on evaluating thermodynamic functions.

To facilitate the study of thermodynamics, it is imperative to grasp certain terminologies employed in this field:

To study and understand thermodynamics it is very essential to understand some terminologies employed in thermodynamics. These terminologies are

1) System: A thermodynamic system is a part of universe which is studied for our observations.

2) Surrounding: Everything apart from the system in the rest of the universe is called the surrounding.

3) Boundary or wall: It is a real or imaginary interface which separates the system and surrounding.

Types of system: There are mainly three different types of systems are observed in thermodynamics, depending on the interaction between the system and surroundings. These are:

1) Open systems: A system which can exchange both matter and energy with the surroundings. Because of these exchanges is neither matter nor energy remain constant in open systems.

2) Closed systems: These systems in which exchange of energy with the surroundings is possible while the transfer of matter with surroundings does not take place. Because of this, in a close system mass remains constant but energy changes.

3) Isolated systems: In these systems there are no exchange of matter and energy between the system and the surroundings. Therefore in this system both mass and energy remain constant.

Systems can also be categorized in another way

Homogeneous system: A system is said to be homogeneous if it is uniform throughout. For example, a gas or a mixture of gases or a pure liquid or a pure solid or a solution of a solid in a liquid are all homogeneous systems such a system is said to have one face only.

Heterogeneous system: If a system is not uniform throughout, it is said to be heterogeneous. It then consists of two or more pages which are separated from each other by definite bounding surfaces. If you common examples of the heterogeneous systems are (a) a system consisting of a liquid and its vapour, (b) to or more immiscible liquids, (c) a mixture of two or more solids.

Macroscopic system: Means a system containing a large amount of substances. In other words, system is one in which there are large number of particles i.e. atoms, ions or molecules.

Microscopic property: A property associated with the collective behaviour of particles in a macroscopic system is called a microscopic property. If you examples of this properties are pressure volume temperature surface tension viscosity density refractive index etc.

There are also several properties of a system. Measurable properties of a system maybe divided into two classes, viz., extensive and intensive.

1) Extensive property:  This property of a system depends upon the total amount of material in the system. Mass, volume, internal energy, heat contents, free energy, entropy, heat capacity are some examples of extensive properties.

2) Intensive property: This property on the other hand is defined as a property which is independent of the amount of material in the system. Density, molar properties, i.e., molar volume, molar energy, molar entropy, molar heat capacity etc., surface tension, viscosity, specific heat, thermal conductivity, refractive index, pressure, temperature, boiling and freezing points, vapour pressure of a liquid, etc., are some intensive properties.

State of a system: A thermodynamic system is said to be in a definite state when the properties have definite values various measurable properties of a system which completely define the state of a system are pressure, volume, temperature and concentration. These are known as the state variables or thermodynamic variables. Any change in the property due to a change in the state of a system depends only on the initial and final state. These variables are directly measurable from experiments and do not require any assumption regarding the structure of matter and related to one another by an equation called equation of state.

For an ideal gas the equation of state for n moles is PV= nRT while for a van der waals gas, the equation of state is (P+an²/V²)(V-nb) = nRT.

The thermodynamic state of a system in such cases can be defined completely by specifying any two of the three variables any change in the value of these variables will change in the state of the system which will attend a new state. If it is desired to bring the system back to its initial state the variables will have their original values.

Change in the state: Change in the state of a system is completely defined when the initial and final states are specified.

Path: It is the sequence of intermediate States or stages arranged in order, followed by the system in going from its initial to the final state.

Thermodynamic equilibrium: A system is said to be in a state of thermodynamic equilibrium if none of the observable properties of the system appears to change with time. The term Thermodynamic Equilibrium assumes the existence of three types of equilibria in the system. They are

1) Thermal equilibrium: This equilibrium demands that there should be no flow of heat from one portion of the system to another. This can happen if the temperature of the system remains constant.

2) Mechanical equilibrium: This equilibrium implies that no work should be done by one part of the system over another i.e. No microscopic movement of matter should occur within the system or of the system with respect to its surroundings. This is possible if the pressure of the system remains constant.

3) Chemical equilibrium: This equilibrium demands that no change in composition should take place in any part of the system with passage of time.

An equilibrium may be stable, metastable or unstable. If after displacement to a new state and release of the constant causing displacement, it goes back to its original state, the system is said to be in a state of stable equilibrium. In metastable equilibrium, the system is stable for smaller displacements and unstable for larger displacements.

Process: A thermodynamic process is defined as the method of operation with the help of which a change in the state of a system is affected. There are various kinds of process and these are:

Cyclic process: If a system after undergoing through a series of changes in its state comes back to its initial state, then the process is turned as cyclic process and the path followed is known as the cyclic path.

Isothermal process: When a process is carried out in such a manner that the temperature remains constant throughout the process, it is called and isothermal process. During this process can flow from the system to the surroundings and vice versa in order to keep the temperature of the system constant.

Adiabatic process: When a process is carried out in such a manner that no heat can flow from the system to the surroundings or vice versa, i.e., the system is completely insulated from the surroundings, it is called and adiabatic process.

Isochoric process: It is a process during which the volume of the system remains constant.

Isobaric process: It is a process during which the pressure of the system remains constant.

Reversible process: A reversible process is when a process is carried out infinitesimally slowly so that all changes occurring in the direct process can be exactly reversed and the system remains almost in a state of equilibrium at all times. In other words, a reversible process may be defined as a process which is conducted in such a manner that at every stage, driving force is only infinitesimally greater than the opposite force and which can be reversed by increasing the opposing force by infinitesimal amount. Reversible process is, therefore, always in a state of equilibrium at each of the small stages. As an example of a reversible process, consider a case in which a system absorbs heat from the surroundings. Reversibility in the case implies that the temperature of the surroundings should be infinitesimally higher than that of the system. If heat is to flow from the system to the surroundings, the temperature of the latter must be only infinitesimally lower than that of the system. Similarly, the expansion of a gas at constant temperature in closed in a cylinder fitted with a weightless and frictionless piston will be reversible only if the pressure on the gas during expansion is reduced by an infinitesimal amount. During compression, the pressure on the gas at each stage is increased by a very small amount.

A truly reversible process has to be carried out in an infinite number of states or stages and would thus require infinite time for its completion. In actual practice, the small changes in a process have definite magnitudes and are only approximately closer to strictly reversible process. Strictly speaking, a reversible process is almost impossible to achieve.

Irreversible process: A process that occurs rapidly or spontaneously such that it does not remain in equilibrium during the transformation is called an irreversible process search process do not involve a succession of equilibrium states of the system. After undergoing a change such processes do not return themselves to their initial state but can be reverse only with the help of external agencies. Expansion of gas against zero applied pressure, dissolution of solute in a solvent, mixing of gases, flow of liquid from higher to lower levels etc. are examples of irreversible process.

Complete differentials

Thermodynamic functions like pressure, volume, temperature, energy, entropy, etc. are state functions. The change in the values of these quantities does not depend on how the change is carried out but depends only on the initial and final states of the system. If Z is any thermodynamic property of a homogeneous system of constant composition then its value is completely determined by the three thermodynamic variables pressure, volume, and temperature. They are related to one another by an equation of state. Any two of these three variables are sufficient to define any thermodynamic property. Therefore we can write,

Z = f(P,T)

Here Z may be energy, volume, enthalpy content or any other property to be considered in details at a later stage. Any change in Z resulting from changes in the values of P and T is given by

ΔZ = Z_final-Z_initial

Utilizing the principle of calculus, we may write for an infinitesimal change dZ in the property Z

ΔZ = (dZ/dP)_TdP +(dZ/dT)_PdT

Where the partial derivatives (dZ/dP)_T represents the rate of change of Z with pressure at constant temperature and (dZ/dT)_P denotes the rate of change of Z with temperature at constant pressure. Therefore, the first term on the right hand side denotes the contribution of change in pressure and the second term indicates the contribution for changes in temperature. The differential dZ of a function Z as defined by this expression is called a complete or exact differential. If we put (dZ/dP)_T = L (P,T) and (dZ/dT)_P = M(P, T), then we get

dZ = L(P,T)dP + M (P,T)dT

On differentiating L(P, T) [=(dZ/dP)_T] with respect to T keeping P constant and M(P, T) [=(dZ/dT)_P] with respect to P maintaining T constant, we get

(dL/dT)_P = d²Z/dTdP

(dM/dP)_T = d²Z/dPdT

d²Z/dTdP = d²Z/dPdT

(dL/dT)_P = (dM/dP)_T

Hence, if Z is any thermodynamic function, dZ is an exact differential then the cross derivatives, (dL/dT)_P and (dM/dP)_T must be equal. This is known as Euler’s theorem of exactness. Another characteristic of an exact differential is that its value for a value for a cyclic transformation is zero, i.e.,

∮dZ = 0

Here, ∮ denotes the cyclic integral.

We can therefore conclude that dZ will be an exact differential when:

(i) Z is a single-valued function depending entirely on the values of temperature and pressure,

(ii) dZ between two specified states is independent of the path of the transformation,

(iii) for a cyclic process ∮dZ = 0

(iv) d²Z/dTdP = d²Z/dPdT

As an example, suppose we have a system containing an ideal gas. The pressure for a given quantity, say one mole, of the gas is a function of temperature and volume of the gas, i.e.,

P = f (T, V)

For dP to be an exact differential, we have

dP = (dP/dT)_VdT + (dP/dV)_TdV

d²P/dTdV = d²P/dVdT

These equations can be evaluated using the ideal gas equation PV = RT. Thus

(dP/dT)_V = R/V and d²P/ dVdT = -R/V²

(dP/dV)_T = -RT/V and d²P/ dTdV = -R/V²

From these equations we can see that

d²P/ dVdT = d²P/ dTdV

Hence dP is an exact differential.

There are other thermodynamic functions which depend only on the state of the state of the system and are therefore state functions.

Cyclic rule: Considering any thermodynamic function of volume V and temperature T, we can write

Z = f (V, T)

Since Z is a state function dZ is given by

dZ = (dZ/dV)_T dV + (dZ/dT)_V dT

dZ = 0

(dZ/dV)_T dV = - (dZ/dT)_V dT

(dZ/dV)_T (dV/dT)_Z = - (dZ/dT)_V

Therefore from rearrangement we get

(dZ/dV)_T (dV/dT)_Z (dT/dZ)_V = -1

This expression represents the cyclic rule. Similar types of expressions can be deduced for any other thermodynamic quantity. For example, if Z is the pressure of a gas, this expression can be written as

(dP/dV)_T (dV/dT)_P (dT/dP)_V = -1

These expressions represents the basic terminology which is very much required to understand  thermodynamics as a subject.

Reference

1) Peter Atkins, Julio de Paula, Atkins’ physical chemistry book, eighth edition.