Introduction:

Thermodynamics is the branch of physics that deals with heat, work, temperature, and energy transfer. A fundamental part of thermodynamics is understanding the state of a system, which is defined using state variables and governed by the equation of state. In this chapter, we’ll explore what these variables mean, how they interact, and how they form the foundation for further thermodynamic laws and processes.

Thermodynamic State Variables and Equation of State – Class 11 Physics:

What Are Thermodynamic State Variables?

State variables are measurable physical quantities that define the state of a thermodynamic system at equilibrium. They provide complete information about the system and include:

• Pressure (P)

• Volume (V)

• Temperature (T)

• Internal Energy (U)

• Entropy (S)

• Enthalpy (H)

Types of Thermodynamic State Variables:

Intensive Variables:

• Do not depend on the size or mass of the system.

• Examples: Pressure, Temperature, Density.

Extensive Variables:

• Depend on the size or amount of substance in the system.

• Examples: Volume, Internal Energy, Entropy.

Note: Extensive variables can be made intensive by dividing them by mass or mole (e.g., specific volume).

Equation of State:

Ideal Gas Equation:

PV = nRT

Where:

P = Pressure

V = Volume

n = Number of moles

R = Universal gas constant (8.314 J/mol·K)

T = Temperature in Kelvin

Difference Between State Variables and Path Variables:

Internal Energy as a State Variable:

Internal energy (U) is the total energy contained in a system due to molecular motion and interactions. It is a state function, meaning its value depends only on the current state of the system and not on how the system arrived there.

In the First Law of Thermodynamics:

ΔU = Q - W

Internal energy change is related to the heat added and the work done by the system.

Graphical Representation of State Variables:

P-V Graph:

• Shows the relationship between pressure and volume.

• Area under the curve gives the work done during expansion or compression.

T-V Graph:

• Useful for understanding heating or cooling processes at constant volume.

Real Gases and Deviation from Ideal Equation:

At high pressure and low temperature, gases deviate from the ideal gas behavior. For real gases, the Van der Waals equation corrects the ideal gas equation:

(P + a/V²)(V - b) = RT

Where:

a and b are constants for intermolecular forces and molecular volume.

Applications of State Variables and Equations of State:

• Designing engines and refrigerators

• Understanding weather systems

• Predicting behavior of gases in chemistry and industry

• Thermodynamic analysis in aerospace

Conclusion:

Understanding thermodynamic state variables and the equation of state forms the basis of learning more advanced concepts in thermodynamics. These variables help us describe the condition of a system quantitatively, and the equations of state allow us to relate them mathematically. Grasping these fundamentals is crucial for solving numerical problems and applying thermodynamic principles in real-life applications.