Jawaharlal Nehru Technological University Hyderabad B.Tech IV BASICS OF THERMODYNAMICS Previous Question Paper (December - 2020 - R16)

In thermodynamics, the distinction between exact and inexact differentials is fundamental to understanding state functions versus path functions.

Exact Differentials: An exact differential, denoted by the symbol d, corresponds to a change in a state function. The integral of an exact differential between two states depends only on the initial and final states, not on the path taken. Mathematically, if a differential dZ is exact, its cyclic integral is zero:

Examples of exact differentials include internal energy (dU), enthalpy (dH), entropy (dS), and pressure (dP). These properties are point functions; they possess a unique value at any given state of the system.

Inexact Differentials: An inexact differential, denoted by the symbol δ, corresponds to a path function. The value of the integral depends on the specific process or path followed between two states. The cyclic integral of an inexact differential is not zero:

Examples of inexact differentials include heat transfer (δQ) and work transfer (δW). These quantities are not properties of the system; they represent energy in transit and are only defined during a process.

Key differences are summarized below:

• Dependence: Exact differentials depend only on end states; inexact differentials depend on the path.
• Mathematical property: Exact differentials are perfect differentials of a state function; inexact differentials are not.
• Cyclic integral: The cyclic integral of an exact differential is always zero, whereas for an inexact differential, it is non-zero.
• Physical significance: Exact differentials represent thermodynamic properties; inexact differentials represent energy interactions.

Thermodynamic properties are macroscopic characteristics of a system that can be measured or calculated to define its state at any given point in time. They are essential because they allow us to quantify the energy content, physical condition, and equilibrium state of a system, enabling the analysis of energy transformations and the performance of thermodynamic cycles.

Thermodynamic properties are primarily classified into two categories:

1. Intensive Properties: These are independent of the mass or size of the system. Examples include temperature, pressure, and density. They are significant because they define the local state of the substance regardless of how much material is present, making them crucial for identifying phase and equilibrium conditions.
2. Extensive Properties: These depend on the mass, size, or extent of the system. Examples include total volume, total internal energy, enthalpy, and entropy. They are significant because they represent the total capacity of a system to perform work or store energy, and they change in direct proportion to the amount of matter in the system.

Specific properties, such as specific volume (volume per unit mass), are derived by dividing an extensive property by the total mass, effectively converting it into an intensive property. This is vital for thermodynamic analysis as it allows for the use of property tables and state equations that are independent of the specific system size. Understanding these properties is necessary to apply the laws of thermodynamics, such as the First Law for energy conservation and the Second Law for determining process directionality and efficiency limits.