# Thermodynamic Properties and Relations

## What are Thermodynamics Properties and Relations?

It is useful to know these quantities separately for each of the materials joining the reaction to carry out a program of finding changes in the different thermodynamic functions that follow reactions such as entropy, enthalpy, and free energy.

If the entropies of the reactants and products are defined independently, the entropy change for the reaction is proportional to the difference.

ΔSreaction = Sproducts − Sreactants

and the other thermodynamic functions in the same direction. Furthermore, if the entropy change for a reaction is known under one set of temperature and pressure conditions, it can be found under other sets of conditions by using entropy variance for the reactants and products as part of the overall phase. For these reasons, scientists and engineers have created detailed tables of thermodynamic properties for a wide range of common compounds, as well as their rates of change as state variables including temperature and pressure change.

The science of thermodynamics includes a variety of formulas and techniques that allow the most knowledge to be derived from a small number of laboratory measurements of material properties.

However, since the thermodynamic state of a system is determined by several variables, such as temperature, strain, and volume, it is important to first determine how many of these variables are independent, and then to define which variables are required to change while others remain constant. As a result, the mathematical framework of partial differential equations is important for promoting the understanding of thermodynamics.

### Maxwell Thermodynamic Relations

Maxwell thermodynamic relations are a series of thermodynamic equations that can be deduced from the symmetry of second derivatives and the concepts of thermodynamic potentials.

These relationships are named after James Clerk Maxwell, a nineteenth-century physicist.

The structure of Maxwell relations is a declaration of equality for continuous functions second derivatives.

It follows directly from the assumption that the order in which two variables' analytic functions are differentiated is meaningless (Schwarz theorem). The function considered in Maxwell relations is a thermodynamic potential, and xi and xj are two separate natural variables for that potential.

$\frac{\delta }{\delta x_{j}}(\frac{\delta \phi }{\delta x_{i} })=\frac{\delta }{\delta x_{i}}(\frac{\delta \phi }{\delta x_{j} })$

where all other natural variables are maintained constant and partial derivatives are measured.

There are (n(n-1))/2 possible Maxwell relations for each thermodynamic potential, where n is the number of natural variables for that potential. According to the laws of thermodynamics, the large rise in entropy would be confirmed.

### Enthalpy

The heat energy consumed or released during a chemical reaction is referred to as enthalpy.

The enthalpy is denoted by the letter H. The letter H stands for the sum of electricity. The change in enthalpy is denoted by the symbol H, where the symbol denotes the change in enthalpy. The enthalpy can be expressed in joules (j) or kilojoules (kj).

Enthalpy is defined as the amount of a system's internal energy. This is since the internal energy of a chemical reaction changes, and this transition is measured as the enthalpy. The enthalpy of a phase occurring at constant pressure can be calculated as follows.

H = U + PV

Where,

H is the enthalpy,

U is the sum of the internal energy

P is the pressure of the system

V is the volume of the system

The enthalpy change of a reaction determines whether it is endothermic or exothermic.

The reaction is endothermic if the value of H is positive. Which ensures that outside energy must be supplied to the system for the reaction to take place. If the H value is negative, however, the reaction is releasing energy to the environment.

Enthalpy transition also happens as a substance's phase or state changes. As a solid is converted to a liquid, for example, the enthalpy changes. This is referred to as fusion heat. The heat of vaporisation is the enthalpy transition that occurs when a liquid is changed to a gaseous state.

### Internal Energy

The sum of a system's potential and kinetic energy is the system's internal energy.

Potential energy is the energy that is retained, and kinetic energy is the energy that is produced as molecules move. The internal energy is denoted by the letter U, and the transition in internal energy is denoted by the letter U.

The enthalpy change in that mechanism is equal to the change in internal energy at constant strain. There are two ways in which internal energy can shift. One is due to heat transfer: the device may either absorb or emit heat to the environment. Both methods have the potential to alter the system's internal capacity. The other way would be to work. Therefore, the change in internal energy can be calculated as follow.

∆U = q + w

Where,

∆U is the change in internal energy,

q is the heat transferred,

w is the work done on or by the system

An isolated device, on the other hand, cannot have a term U because internal energy is constant, energy transfer is zero, and no work is performed.

When the value of U is positive, it means that the device receives heat from the environment and that testing is being performed on it. When the U value is negative, the machine releases heat and operates.

Internal energy, on the other hand, may occur as potential or kinetic energy but not as heat or function. This is because heat and function only exist while the system is changing.

## Relation Between Internal Energy and Enthalpy

 Enthalpy Internal Energy Enthalpy is the heat energy that is being absorbed or evolved during the progression of a chemical reaction. The internal energy of a system is the sum of potential energy and kinetic energy of that system. Calculated as H = U + PV Calculated asΔU = q + w Enthalpy is defined as the relationship between the system and the surrounding. Internal energy defined as the total energy in a system.

1. What is the Relation Between Enthalpy and Temperature?

Answer: The number of molecular interactions increases as the temperature rises.

The intrinsic energy of the mechanism increases as the number of connections increases. According to the first equation, as the temperature rises, the internal energy (U) increases, and the heat (H) increases.

In addition, the enthalpy temperature relationship is, When the temperature of a system increases, the kinetic and potential energies of the atoms and molecules in the system increase. Thus, the internal energy of the system increases, which means that the enthalpy of the system increases.

2. What is the Relation Between Heat Capacities?

Answer: The heat capacity at constant volume, Cv , and the heat capacity at constant pressure, Cp in thermodynamics, is comprehensive properties with the magnitude of energy divided by temperature.

Hence  Cv = T(δS/δT)v and Cp = T(δS/δT)p

Where

T: temperature

V: volume

P: pressure

S: Entropy

3. How are Thermodynamic Properties Classified?

Answer: Thermodynamic properties are classified as either intensive or extensive. If a property is intensive, it is independent of the amount of mass present; if it is a function of the amount of mass present, it is vast. Gravity, temperature, and density are intensive properties, while volume and mass are comprehensive properties.