Thermodynamics: Systems and Forms of Energy Notes

Systems and Boundaries

System: part of the universe on which the analysis is focused.
Environment/surrounding: the rest of the universe outside the system.
Boundary: separates the system from the environment (could be a real physical boundary or an imaginary one).
Real-life approximations include various boundary types and couplings; examples shown in the transcript include closed or isolated cases, with or without mechanical coupling.

Open, Closed, and Isolated Systems; Energy Exchange

Open system: exchanges both matter and energy with the environment (not detailed in the transcript, but commonly defined in thermodynamics).
Closed system: does not exchange substances with the environment; can exchange energy with the environment.
- Energy exchange mechanisms include Heat (q) with the environment.
- If there is mechanical coupling (e.g., a frictionless piston), the system can also exchange energy as Work (w).
Isolated system: does not exchange energy or substances with the environment.
Summary from the transcript: We will mostly focus on closed or isolated systems, with or without mechanical coupling.

Energy Exchange and Forms of Energy

Energy exchanges occur in the form of Heat (q) and Work (w).
Closed or isolated systems are described in terms of energy exchange capabilities:
- Closed systems can exchange energy as Heat with the environment.
- Isolated systems do not exchange energy with the environment.
- Mechanical coupling (e.g., frictionless piston) allows energy exchange as Work with the environment.

Forms of Energy and Units (Recurring Terms)

All forms of energy are measured in Joules (J).
Basic relationships and recurring terms:
- Force × Distance = N × m = [J]
- Mass × Velocity² = kg × (m/s)² = [kg·m²·s⁻²] = [J]
- Pressure × Volume = Pa × m³ = N/m² × m³ = N·m = [J]
- Gas constant × Temperature = R × T = J·mol⁻¹ × K = J/mol
- Temperature × Entropy = T × S = J·mol⁻¹ × K = J/mol
- Planck’s constant × Frequency = h × ν = (kg·m²·s⁻¹) × s⁻¹ = kg·m²·s⁻² = [J]
Note: These relationships illustrate how different physical quantities combine to yield energy units.

Macroscopic Kinetic Energy

Formula: $E_k = frac{1}{2} m v^2$
Example from the transcript:
- A macroscopic body with mass $m = 5000\ ext{kg}$ moving at $v = 65\ ext{mph}$
- Convert velocity: $65\ \text{mph} \approx 29.0\ \text{m/s}$
- Kinetic energy: $E_k = \tfrac{1}{2} \times 5000\ \, \text{kg} \times (29.0\ \, \text{m/s})^2 \approx 2.11 \times 10^6\ \, \text{J}$

Potential Energy (Macroscopic Examples)

Potential energy formula: $E_{ ext{pot}} = m g h$
Example from transcript:
- Initial height $h1 = 3\ \text{m}$, final height $h0 = 0\ \text{m}$, mass $m = 0.1\ \text{kg}$, $g = 9.81\ \text{m s}^{-2}$
- Change in potential energy: $E{ ext{pot, before}} - E{ ext{pot, after}} = m g (h1 - h0) = 0.1 \times 9.81 \times 3 = 2.94\ \, \text{J}$
This illustrates how height changes affect potential energy in simple systems.

Kinetic and Potential Energy in Molecular Systems

In an isolated system, the sum of kinetic and potential energy is constant:
- $Ek^{\text{in}} + E{ ext{pot}}^{\text{in}} = U$
Internal energy ($U$) interpretation:
- Sum of all intermolecular interactions in the system, including:
- Electrostatic interactions
- Hydrogen bonds
- Dipole–dipole interactions
- (\pi)-stacking interactions
- London dispersion (van der Waals) interactions
- Pauli repulsions (exchange repulsion)
Per Degree of Freedom (DOF) energy under classical equipartition:
- $E{\text{kin, 1DOF}} = \tfrac{1}{2} kB T$
- Translations: 3 DOF for every molecule
- Rotations:
- Nonlinear molecules: 3 DOF
- Linear molecules: 2 DOF
- Monoatomic molecules: 0 DOF
These DOF contribute to the overall kinetic energy of the system and relate temperature to microscopic motion.

Thermodynamics: Energy Exchange Between System and Environment

Thermodynamics describes the exchange of energy in the form of or between components of the system and/or the system and its environment.
Examples of processes involving energy exchange: chemical reactions, biomolecular processes, and other events occurring anywhere.
This framework emphasizes how energy flows drive changes in systems, including biological contexts.

Summary of Key Concepts and Connections

Systems, boundaries, and surroundings define the scope of analysis in thermodynamics.
Open, closed, and isolated classifications describe whether matter and energy cross the boundary:
- Open: exchanges matter and energy.
- Closed: exchanges energy (heat, and possibly work if mechanically coupled) but not matter.
- Isolated: exchanges neither energy nor matter.
Energy forms include kinetic and potential energy, with total energy (internal energy) accounting for all micro-level interactions.
The fundamental energy expressions and units connect macroscopic measurements to molecular behavior:
- Kinetic energy: $E_k = \tfrac{1}{2} m v^2$
- Potential energy: $E_{ ext{pot}} = m g h$
- Internal energy: $U = \text{sum of all interactions}$
- Per-DOF energy: $E{\text{kin, 1DOF}} = \tfrac{1}{2} kB T$
DOF counts determine how energy is partitioned among translational and rotational motions:
- Translations: 3 DOF
- Rotations: nonlinear 3 DOF, linear 2 DOF, monoatomic 0 DOF
Energy exchange descriptions illustrate how systems evolve in real and biological contexts:
- Heat (q) and Work (w) are the primary energy transfer mechanisms across boundaries.
- Boundary definitions and mechanical coupling determine whether work can be exchanged.
Recurring energy terms help interpret various energy forms in a unified framework:
- $F \cdot d = \text{J}$
- $P V = \text{J}$
- $R T = \text{J/mol}$
- $T S = \text{J/mol}$
- $h \nu = \text{J}$
The material connects microscopic interactions to macroscopic observables, reinforcing why thermodynamics matters in biology and chemistry.