Key Thermodynamic Relations and Their Real-World Applications
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.
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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.
Relation Between Enthalpy and Internal Energy
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
FAQs on Thermodynamic Properties and Relations Made Easy
1. What are thermodynamic properties and how are they classified?
Thermodynamic properties are characteristics of a system that help define its state, such as temperature, pressure, volume, and internal energy. These can be classified as intensive properties (independent of the amount of matter, like temperature, pressure, and density) and extensive properties (dependent on the amount of matter, like mass and volume).
2. What is meant by a thermodynamic relation in Physics?
A thermodynamic relation is a mathematical equation that connects various thermodynamic properties of a system. For example, Maxwell relations link different partial derivatives of thermodynamic potentials, offering a way to calculate changes in entropy, enthalpy, and internal energy under varying conditions.
3. Explain the difference between enthalpy and internal energy in a thermodynamic system.
Internal energy (U) of a system includes the sum of all microscopic energies (kinetic + potential) within the system, while enthalpy (H) is the total heat content, given by the equation H = U + PV, where P is pressure and V is volume. Enthalpy is particularly useful in processes occurring at constant pressure.
4. How do heat capacity at constant pressure (Cp) and at constant volume (Cv) differ, and what is their significance?
Heat capacity at constant pressure (Cp) is the amount of heat required to raise the temperature of a system by one degree at constant pressure, whereas heat capacity at constant volume (Cv) is measured at constant volume. Usually, Cp > Cv because, at constant pressure, the system can do work as it expands.
5. What are Maxwell’s thermodynamic relations and why are they important?
Maxwell’s relations are a set of equations derived from the properties of thermodynamic potentials. They allow the calculation of otherwise difficult-to-measure properties, such as entropy and temperature changes, in terms of observable quantities. These relations are based on the equality of mixed partial derivatives and are vital for linking different state functions in thermodynamics.
6. Why is enthalpy change important in chemical reactions as per the CBSE syllabus?
The enthalpy change (ΔH) indicates whether a reaction is endothermic (absorbs energy, ΔH positive) or exothermic (releases energy, ΔH negative). This helps predict heat flow during reactions, which is crucial for understanding and controlling chemical processes as required by the CBSE class 12 Physics syllabus (2025-26).
7. How does the concept of entropy apply to spontaneous processes in thermodynamics?
Entropy (S) is a measure of disorder or randomness of a system. In spontaneous processes, the total entropy of the system and surroundings increases. This principle helps predict the direction of natural processes and is fundamental to the Second Law of Thermodynamics.
8. How do changes in temperature affect enthalpy and internal energy of a system?
As temperature increases, both internal energy (U) and enthalpy (H) of a system generally increase due to increased molecular motion and potential energy. This relationship helps explain why heat addition at different conditions affects state variables differently.
9. What role do partial derivatives play in understanding thermodynamic functions?
Partial derivatives enable the study of how one thermodynamic property changes with respect to another while keeping other variables constant. They are essential in forming relations like those found in Maxwell’s equations, allowing precise predictions of changes in state functions.
10. If the enthalpy of a reaction is positive, what does it imply about the energy changes involved?
A positive enthalpy change (ΔH > 0) means the reaction is endothermic, so energy must be supplied for the reaction to proceed. This energy is usually absorbed as heat from the surroundings.
11. In what situations is the internal energy of a system considered constant?
Internal energy remains constant in an isolated system where there is no exchange of energy or matter with the surroundings, meaning both heat (q) and work (w) are zero and ΔU = 0.
12. How can thermodynamic tables be used in solving problems related to property changes?
Thermodynamic tables list standard values of properties like enthalpy, entropy, and internal energy for common substances at different temperatures and pressures. These tables help in accurately calculating changes during chemical reactions and phase transitions as per syllabus problem-solving requirements.
