Summary of Fundamentals of Thermodynamics
Fundamentals of Thermodynamics: A Student's Guide
Introduction
Thermodynamics is the study of energy, its transformations, and how those transformations govern physical and chemical processes. This unit covers core concepts needed to reason about energy changes in matter: types of energy, systems and surroundings, the First and Second Laws of Thermodynamics, state versus path functions, entropy, spontaneity, and how to compute thermodynamic quantities from standard data.
Definition: A system is the portion of the universe chosen for study; the surroundings are everything else; the universe is system plus surroundings.
1. Energy: forms and definitions
Energy is the ability to do work or transfer heat.
1.1 Types of energy
- Kinetic energy (KE): energy due to motion. Example formula: $\mathrm{KE} = \tfrac{1}{2}mv^2$.
- Potential energy (PE): energy due to position or configuration. Example gravitational potential: $\mathrm{PE} = mgh$.
- Internal energy (U): sum of microscopic kinetic and potential energies of particles in the system (translations, rotations, vibrations and interaction energies). For most laboratory-scale systems at rest, total energy $E = U$.
Definition: Internal energy, $U$, is the total microscopic energy contained within a system originating from molecular motion and interactions.
1.2 Important relationships
- Total energy: $E = U + \mathrm{KE} + \mathrm{PE}$. In many chemical problems $\mathrm{KE}=\mathrm{PE}=0$ so $E=U$.
2. System, surroundings and the universe
- Open system: matter and energy can cross the boundary.
- Closed system: only energy can cross the boundary (no mass transfer).
- Isolated system: neither energy nor matter is exchanged.
Table: system types comparison
| System type | Mass exchange | Energy exchange | Example |
|---|---|---|---|
| Open | Yes | Yes | Boiling pot without lid |
| Closed | No | Yes | Sealed, heatable flask |
| Isolated | No | No | Ideal thermos bottle (approx.) |
3. The First Law of Thermodynamics
Definition: The First Law states that energy is conserved: the change in internal energy of a system equals heat added to the system plus work done on the system.
Expressed mathematically: $$\Delta U = q + w$$
- Here $q$ is heat added to the system (positive when added), and $w$ is work done on the system (positive when done on the system).
- Common sign convention in chemistry: work of expansion against external pressure is $w = -P_{ext}\Delta V$ (work done by the system is negative).
Practical example: heating a sealed container at constant volume. If you add heat $q$ and no pressure–volume work occurs ($\Delta V=0$), then $$\Delta U = q_{V}.$$
4. State functions vs path functions
- State functions: properties that depend only on the current state, not the path taken (examples: $U$, enthalpy $H$, entropy $S$, pressure $P$, temperature $T$).
- Path functions: depend on the way the process occurs (examples: heat $q$, work $w$).
Table: state vs path
| Property | State or Path? | Notes |
|---|---|---|
| $U$ | State | depends on state variables only |
| $H$ | State | enthalpy is a state function |
| $S$ | State | entropy is a state function |
| $q$ | Path | depends on process route |
| $w$ | Path | depends on how work is performed |
Definition: A state function is a property whose change depends only on initial and final states. A path function depends on the process taken between states.
5. Enthalpy, entropy and Gibbs free energy (definitions)
- Enthalpy ($H$): $H = U + PV$. Useful for processes at constant pressure.
Definition: Enthalpy, $H$, is a thermodynamic state function equal to $U + PV$.
- Entropy ($S$): measures the number of accessible microstates or the
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Thermodynamics Fundamentals
Klíčové pojmy: Energy types: internal, kinetic, potential, System types: open, closed, isolated, First Law: $\Delta U = q + w$, State vs path functions: $U,H,S$ vs $q,w$, Enthalpy: $H = U + PV$, Entropy increases for spontaneous processes: $\Delta S_{univ}>0$, Gibbs free energy: $\Delta G = \Delta H - T\Delta S$, Predict $\Delta S$ from volume, temperature, particle number changes, Use $\Delta S = \Delta H_{rev}/T$ for reversible isothermal heat exchange, Standard molar entropies: $\Delta S^\circ_{rxn} = \sum n S^\circ_{products} - \sum n S^\circ_{reactants}$