Thermodynamics relies on state variables to describe systems at equilibrium. These properties, like temperature and pressure, are independent of how the system got there. They're crucial for calculating energy, enthalpy, and entropy.

Thermodynamic properties are either intensive or extensive. Intensive properties, like temperature, don't depend on system size. Extensive properties, like volume, do. The ideal gas law and other equations of state help us understand how these properties relate in different substances.

State Variables and Properties

State variables in thermodynamic systems

• Properties that describe the state of a thermodynamic system at equilibrium
  • Temperature, pressure, volume, and mass
• Independent of the path taken to reach the current state
  • System's history does not affect the current values of state variables
• Used to determine the thermodynamic properties of a system
  • Internal energy, enthalpy, and entropy can be calculated using state variables

Intensive vs extensive properties

• Thermodynamic properties classified as either intensive or extensive
• Intensive properties independent of the system size or the amount of matter present
  • Temperature, pressure, and density
  • Remain constant when a system is divided into smaller subsystems
• Extensive properties depend on the size of the system or the amount of matter present
  • Volume, mass, and total energy
  • Additive, meaning they can be summed when combining subsystems

Ideal Gas Law and Equations of State

Applications of ideal gas law

• Equation of state that describes the behavior of an ideal gas
  • Ideal gases are hypothetical gases that perfectly follow the assumptions of the kinetic-molecular theory
• Expressed as $PV = nRT$, where:
  • $P$ is the pressure of the gas
  • $V$ is the volume of the gas
  • $n$ is the number of moles of the gas
  • $R$ is the universal gas constant ($8.314 \frac{J}{mol \cdot K}$)
  • $T$ is the absolute temperature of the gas in Kelvin
• Used to calculate any of the four variables ($P$, $V$, $n$, or $T$) when the other three are known

Equations of state for substances

• Real gases and other substances deviate from ideal behavior, especially at high pressures and low temperatures
• Mathematical models that describe the relationship between state variables for real substances
  • Account for the intermolecular forces and the finite volume occupied by the molecules
• Examples:
  1. Van der Waals equation: $\left(P + \frac{a}{V^2}\right)(V - b) = RT$
     • $a$ and $b$ are substance-specific constants that account for intermolecular attractions and molecular volume, respectively
  2. Redlich-Kwong equation: $P = \frac{RT}{V-b} - \frac{a}{\sqrt{T}V(V+b)}$
     • $a$ and $b$ are again substance-specific constants
• Provide more accurate descriptions of real gas behavior compared to the ideal gas law, especially at high pressures and low temperatures