## Thermodynamic State Variables and Equation of State – Class 11 | Chapter – 12 | Physics Short Notes Series PDF for NEET & JEE

Thermodynamic State Variables: Thermodynamic state variables are physical quantities that describe the state of a thermodynamic system. These variables are used to define the macroscopic properties of a system, such as temperature, pressure, volume, and internal energy, which are important for understanding how the system behaves and changes under different conditions. The state of a system can be described using a set of state variables, which depend on the type of system being studied and the level of detail required. Some common examples of state variables include:

• Temperature (T) – a measure of the average kinetic energy of the particles in a system.
• Pressure (P) – the force exerted by a gas or liquid per unit area.
• Volume (V) – the amount of space occupied by a system.
• Internal energy (U) – the total energy of a system due to the motion and interactions of its particles.
• Entropy (S) – a measure of the disorder or randomness of a system.
• Enthalpy (H) – the total energy of a system plus the energy required to create or destroy it.
• Gibbs free energy (G) – the amount of energy available to do work in a system at constant temperature and pressure.

These state variables can be used to calculate other properties of a system, such as heat capacity, work, and chemical potential, and to understand the behavior of the system under different conditions, such as changes in temperature, pressure, or composition.

## Thermodynamic State Variables

In thermodynamics, variables can be classified as either intensive or extensive, depending on how they change with the size or amount of the system being studied.

• Extensive variables: These variables depend on the size or amount of the system. Examples of extensive variables include mass (m), volume (V), energy (E), and enthalpy (H). If the system is divided into two equal parts, then the extensive variable will also be divided in half. In other words, the extensive variable is additive, meaning it increases with the size or amount of the system. For example, if you double the size of a system, the mass, volume, and energy will also double.
• Intensive variables: These variables do not depend on the size or amount of the system. Examples of intensive variables include temperature (T), pressure (P), and density (ρ). If the system is divided into two equal parts, the value of the intensive variable remains the same for both parts. In other words, the intensive variable is not additive, meaning it is independent of the size or amount of the system. For example, if you double the size of a system, the temperature and pressure will remain the same.

It is important to note that some variables can be both extensive and intensive, depending on how they are defined. For example, specific volume (v = V/m) is an extensive variable because it depends on the volume and mass of the system, but it is also an intensive variable because it is independent of the size of the system once the mass is fixed. Similarly, specific heat (c = Q/mΔT) is an extensive variable because it depends on the heat and mass of the system, but it is also an intensive variable because it is independent of the size of the system once the mass is fixed.

### Equations of state

These equations make it easier to determine the properties of a system. There are certain equations of state. Some of them are:

• Ideal gas law: This is the most fundamental equation that relates pressure, volume, temperature, number of moles, and the universal gas constant with each other. It states that

PV=nRT.

• Lee-Kesler Generalised Correlation: This is used to calculate Z as a function of reduced temperature (Tr) and reduced pressure (Pr). Tr and Pr are computed by dividing the temperature and pressure of the gas by its critical temperature (Tr=T/Tc) and critical pressure (Pr=P/Pc). Another solution is found out using compressibility charts. It is expressed as

PV = ZnRT.

• Van-der Waals Law: This law modifies the ideal gas law and deals with natural gases. Here, the coefficients are determined using empirical relations. The law says that

P = RT/(VM – b) – a/VM2

Where ‘a’ represents the attractive interactions in the gas, and ‘b’ represents the repulsive interactions or the molecular volume of the gas particles. VM represents molar volume or volume per mole and T is temperature.

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