Thermodynamics

1. State Functions vs. Path Functions
   1. State Functions
      1. Definition and Characteristics
         1. Independent of the path taken
         2. Depend only on the current state of the system
         3. Examples of state functions
      2. Examples
         1. Enthalpy (H)
            1. Relationship with internal energy
            2. Dependence on pressure and volume changes
         2. Entropy (S)
            1. Measure of disorder or randomness
            2. Implications in second law of thermodynamics
         3. Internal Energy (U)
            1. Sum of kinetic and potential energy at the microscopic level
            2. Changes described by the first law of thermodynamics
         4. Other Examples
            1. Gibbs Free Energy
               1. Role in spontaneity of chemical reactions
               2. Temperature and pressure dependence
            2. Helmholtz Free Energy
               1. Application in constant volume processes
            3. Volume (V)
               1. Function of state variables like temperature and pressure
            4. Pressure (P)
            5. Temperature (T)
      3. Properties
         1. Extensive vs. Intensive State Functions
            1. Extensive: Depend on the size/extent of the system (e.g., enthalpy, internal energy)
            2. Intensive: Independent of system size (e.g., temperature, pressure)
   2. Path Functions
      1. Definition and Characteristics
         1. Depend on the path taken between initial and final states
         2. Cannot be described by a change in state value
         3. Often associated with processes or transformations
      2. Examples
         1. Heat (Q)
            1. Energy transfer due to temperature difference
            2. Associated with the second law of thermodynamics
            3. Heat transfer mechanisms
         2. Work (W)
            1. Energy transfer due to force acting through a distance
            2. Types of work (e.g., expansion, electrical, mechanical)
         3. Differences between heat and work
      3. Calculating Path Functions
         1. Use of path integral: \(\int dq = \int \delta W + \int \delta Q\)
         2. Dependent on specifics of the path or process conditions
      4. Relationships with State Functions
         1. First Law of Thermodynamics: \(\Delta U = Q - W\)
            1. State functions can be derived from path functions
            2. Illustrates interplay between energy changes, work, and heat