Thermochemistry

Definition: Thermochemistry is the study of chemistry involving heat changes during chemical processes.
Heat Changes: These changes can occur between different components of a system, referred to as components of the environment.

Labels for Objects:
- System: The primary focus, which can vary depending on the context:
- Physician: The patient in front of them.
- Mayor: The city they govern.
- President: The country they lead.
- Chemist: The beaker of chemicals being analyzed.
- Surroundings: Everything external to the system (e.g., the room for a patient, neighboring city for a mayor, etc.).
- Universe: The sum of the system and surroundings, not a third distinct entity.

Types of Energy Transfer:
- Work (W): Can be lost (negative W) or gained (positive W) with respect to the system.
- Heat (Q): Can also be lost (negative Q) or gained (positive Q) concerning the system.

Open System:
- Exchanges both matter and energy with its surroundings.
- Example: The ocean (water cycle and energy exchange with the sun).
Closed System:
- Exchanges only energy but not matter with its surroundings.
- Example: A coffee cup that cools down but does not spill.
Isolated System:
- Does not exchange either matter or energy with the surroundings.
- Example: A thermos flask is designed to minimize heat and matter exchange (pseudo-isolated).
- True isolated system: The universe itself.

Reversible Process:
- A system can return to its initial state (e.g., going from state 1 to state 2 and back to state 1).
- Equilibrium States: No driving force exists when paused at any point in between.
Irreversible Process:
- A system cannot return to its original state without changes (e.g., going from state 1 to state 2 and then to state 1').
- Results in a distinct final state that does not match the initial state.

Work (W): Defined generally as the sum of incremental forces applied over distances. Mathematically represented as:
- $W = \text{(Force)} \times \text{(Distance)}$
- Derived further as $W = - P \times dV$ (where P is pressure, and dV is the change in volume).
Path Function vs. State Function:
- Path Function: Dependent on the path taken (work is a path function; does not store history).
- State Function: Depends only on initial and final states (e.g., potential energy).
- Example:
- Two hikers take different paths up a mountain but reach the same height, resulting in identical changes in potential energy.

Constant Pressure Work:
- If the pressure remains constant while volume changes, specific equations measure work but can overestimate or underestimate it.
- The area under the pressure-volume curve represents work.
Variable Pressure Work:
- Work is calculated over changes in pressure during changes in volume.
- Using the ideal gas law, substituting pressure can lead to the equation:
- $W = -nRT \times \text{log}(V<em>f / V</em>i)$ (where n = moles, R = ideal gas constant, T = temperature).

Discovery: Relates changes in internal energy to heat and work.
Equation: $\text{dU} = Q + W$ (where dU is the change in internal energy, Q is heat added, and W is work done).
Distinction Between Heat and Work:
- Heat (Q): Involves chaotic molecular motion, considered invisible as it moves in various directions.
- Work (W): Involves uniform motion, much easier to observe.
Heat Capacity (C):
- Relates heat absorbed or released to the change in temperature.
- $Q = C \Delta T$ (where C is the heat capacity and $\Delta T$ is the change in temperature).
- For specific heat capacity: $Q = mc \Delta T$ (where m is mass and c is specific heat capacity).
Enthalpy (H):
- Represents the total heat content of a system at constant pressure.
- Defined as $H = U + PV$ (where U is internal energy, P is pressure, and V is volume).
- Change in enthalpy at constant pressure: $\Delta H = \Delta U + P\Delta V$ (often used to measure heat flow in chemical reactions).