Thermodynamic Terms

Thermodynamics: Thermodynamics is the branch of physics and chemistry that deals with heat, work, temperature, and energy. It describes how energy is transferred and transformed in physical and chemical processes. It is concerned with macroscopic properties of matter and energy, and does not delve into the microscopic details of individual atoms or molecules.

The System And The Surroundings

The System: In thermodynamics, the system is defined as the specific part of the universe that is being studied or considered. It is the region of space or the quantity of matter that we are focusing on.

Examples: A chemical reaction in a beaker, a gas in a cylinder, a living organism, or even the entire universe.

The Surroundings: The surroundings comprise everything else in the universe that is outside the system. The system and surroundings are separated by a boundary.

Examples: If the system is a beaker with a chemical reaction, the surroundings would be the air in the room, the bench, the person observing, etc.

Boundary: The boundary is the real or imaginary surface that separates the system from its surroundings. The nature of the boundary determines the type of interaction that can occur between the system and surroundings (e.g., transfer of energy or matter).

Types Of The System

Systems are classified based on the type of exchange they can have with their surroundings:

Isolated System:
- Definition: A system that cannot exchange either energy (heat or work) or matter with its surroundings.
- Boundary: An impermeable and adiabatic boundary.
- Examples: An idealized perfectly insulated container (like a thermos flask with a perfect seal and insulation), or the universe as a whole (assuming it is isolated).
Closed System:
- Definition: A system that can exchange energy (heat or work) with its surroundings, but not matter.
- Boundary: An impermeable but diathermal (allowing heat transfer) or capable of doing work boundary.
- Examples: A gas contained in a cylinder with a movable piston (work can be done on or by the gas, and heat can be transferred, but the gas itself stays inside). A sealed bottle of water.
Open System:
- Definition: A system that can exchange both energy (heat or work) and matter with its surroundings.
- Boundary: A permeable and diathermal boundary.
- Examples: A pot of boiling water without a lid (heat and steam/water vapor are exchanged), a living cell, a car engine.

The State Of The System

State Variables (State Functions): The state of a system is defined by its observable macroscopic properties, called state variables or state functions. These are properties that have definite values for a given system under a specific set of conditions.

Common State Variables:

Pressure (P): Force per unit area.
Volume (V): The space occupied by the system.
Temperature (T): A measure of the average kinetic energy of the particles.
Amount of Substance (n): The quantity of matter in the system, often measured in moles.
Internal Energy (U): The total energy contained within the system.
Entropy (S): A measure of the disorder or randomness of the system.
Enthalpy (H): A thermodynamic potential that accounts for the internal energy of the system plus the energy required to establish its volume at any given pressure and temperature ($H = U + PV$).
Gibbs Free Energy (G): A thermodynamic potential that can be used to calculate the maximum amount of non-expansion work that can be extracted from a closed system at constant temperature and pressure ($G = H - TS$).

State Function: A property that has a value that depends only on the current state of the system, not on the path taken to reach that state. For example, the change in altitude from point A to point B is independent of the route taken.

Path Function: Properties that depend on the path taken to reach a state. Heat ($q$) and Work ($w$) are path functions, not state functions.

State of Equilibrium: A system is in a state of thermodynamic equilibrium when its macroscopic properties (like P, V, T) are constant over time, and there is no net flow of matter or energy between the system and its surroundings. For a system to be completely defined, its state variables must be specified.

The Internal Energy As A State Function

Internal Energy (U): The internal energy ($U$) of a system is the total energy contained within the system. It is the sum of all the microscopic energies of the system's components.

Internal Energy includes:

Kinetic Energy: Associated with the motion of molecules (translation, rotation, vibration).
Potential Energy: Associated with the intermolecular forces and intramolecular forces (chemical bonds) within the system.
Electronic Energy, Nuclear Energy, etc.

Internal Energy as a State Function:

The internal energy ($U$) is a state function. This means that the change in internal energy ($\Delta U$) between two states (initial state $i$ and final state $f$) depends only on these states and not on the path or process by which the system goes from state $i$ to state $f$.

$$\Delta U = U_f - U_i$$

First Law of Thermodynamics: The first law of thermodynamics quantifies the change in internal energy. It states that the change in internal energy ($\Delta U$) of a system is equal to the heat ($q$) added to the system plus the work ($w$) done on the system.

$$\Delta U = q + w$$

Sign Conventions:

Heat ($q$):

$q > 0$: Heat is absorbed by the system (endothermic process).
$q < 0$: Heat is released by the system (exothermic process).

Work ($w$):

$w > 0$: Work is done ON the system (e.g., compression of a gas).
$w < 0$: Work is done BY the system (e.g., expansion of a gas against external pressure).

Path Dependence of Heat and Work: Although $\Delta U$ is a state function, the individual components $q$ and $w$ are path functions. This means that the amount of heat transferred and work done can vary depending on the process (the path) connecting the initial and final states, but their sum ($q+w$) will always be the same for a given change of state.

Example: Consider a gas in a cylinder that expands from an initial volume $V_1$ to a final volume $V_2$. This expansion can occur in different ways (e.g., at constant pressure, at constant temperature). In each case, the initial and final states might be the same, leading to the same $\Delta U$, but the amounts of heat absorbed ($q$) and work done by the system ($w$) will be different depending on the path.