The Arrow of Entropy

NODE 01

The Thermodynamic View

• System: Part of universe being studied.
• Surroundings: Everything else.
• Boundary: Separates them.

NODE 02

Types of Systems

• Open: Mass & Energy cross boundary.
• Closed: Only Energy crosses.
• Isolated: Neither crosses.

NODE 03

Thermodynamic State

P, V, TPV = nRT

• Macroscopic variables describe the system.
• Pressure, Volume, Temp, Internal Energy.
• Ideal-gas state relation.

NODE 04

State Variables

• Depends ONLY on the current state.
• P, V, T, U.
• State function ≠ path-dependent quantity.

NODE 05

Path Variables

• Depend on the process used to move between states.
• Heat (Q) and Work (W).
• Same initial/final state, different Q and W.

NODE 06

Thermo Processes

ISOTHERMALADIABATICISOBARICISOCHORICCYCLIC

• Isothermal (T const), Adiabatic (Q=0).
• Isobaric (P const), Isochoric (V const).

NODE 07

P-V Diagrams

• Pressure vs Volume.
• Area under P-V curve = Work done by system.
• W = ∫P dV.

NODE 08

Work Done by Gas

• Constant pressure: W = PΔV.
• Expansion: System does positive work.
• Compression: Work done on system.

NODE 09

Internal Energy (U)

• Microscopic energy stored within system.
• Molecular motion, interactions, configs.
• Ideal gas: U depends ONLY on Temp.

NODE 10

Heat vs Work

• Heat = transfer due to temp difference.
• Work = transfer via force/displacement.
• Neither is a substance INSIDE the system.

NODE 11

The First Law

ΔU=Q-W

• Central accounting law. Energy conservation.
• Energy supplied (Q/W) changes internal energy (U).
• (W defined as work done BY system).

NODE 12

First-Law Cases

Const V: Q = ΔUAdia: ΔU = -WIsol: ΔU = 0Cylic: ΔU = 0

• Isochoric (W=0), Adiabatic (Q=0).
• Isolated (Q=0, W=0).
• Cyclic (Final state = Initial, so ΔU=0).

NODE 13

Heat Capacity Gases

Cp-Cv=R

• Cv = Heat cap at constant volume.
• Cp = Heat cap at constant pressure.
• γ = Cp/Cv (useful in adiabatic).

NODE 14

Ideal-Gas Int Energy

U = 3/2 nRT(Monatomic)

• U depends on temperature.
• ΔU = 3/2 nRΔT.
• Connects thermo to molecular picture.

NODE 15

Isothermal Process

• T = constant. PV = constant.
• Expansion: P drops, V rises, T stays same.
• W = nRT ln(V₂/V₁).

NODE 16

Adiabatic Process

• Q = 0. (No heat transfer).
• PVᵞ = constant. TV^(γ−1) = constant.
• Expansion cooling, Compression heating.

NODE 17

Isobaric Process

• P = constant.
• W = P(V₂ - V₁).
• Heating at constant pressure causes volume change.

NODE 18

Isochoric Process

• V = constant. W = 0.
• Therefore: Q = ΔU.
• Heating in a rigid container.

NODE 19

Cyclic Processes

• System returns to original state (ΔU = 0).
• Whole cycle: Q_net = W_net.
• Foundation of heat-engine analysis.

NODE 20

Rev vs Irreversible

vs

• Reversible: Idealized, restores system/surroundings.
• Irreversible: Real processes (friction, mixing).
• Real processes have a preferred direction.

NODE 21

The Second Law

• Heat flows Hot → Cold naturally.
• No cyclic engine converts 100% heat to work.
• Real processes generate entropy.

NODE 22

Heat Engines

• Converts part of incoming heat into work.
• Hot res (QH) → Engine (W) → Cold res (QL).
• QH = W + QL.

NODE 23

Thermal Efficiency

η = W / QH=1 - (QL/QH)(η < 1)

• Useful Work / Input Heat.
• η < 1 for ordinary cyclic heat engines.

NODE 24

Carnot Engine

• Ideal reversible heat engine.
• Iso-T Exp → Adia Exp → Iso-T Comp → Adia Comp.
• η = 1 - (Tc/Th). The absolute upper limit.

NODE 25

Refrigerators

• Uses WORK to move heat Cold → Hot.
• Cold res (QL) → Fridge (W in) → Hot res (QH).

NODE 26

COP

COP_ref =QL/W

• Coefficient of Performance.
• COP = QL / W (Refrigerator).
• COP can exceed 1 (unlike efficiency).

NODE 27

Heat Pump

COP_hp =QH/W

• Focuses on useful heating rather than cooling.
• Building heating, climate control.

NODE 28

Entropy (S)

dS=δQ_rev/T

• Central concept. State function.
• Units: J/K.

NODE 29

Entropy & 2nd Law

ΔS_univ≥0

• For an isolated system: ΔS ≥ 0.
• Entropy of universe does not decrease in real processes.
• Can decrease locally if generated elsewhere.

NODE 30

The Arrow of Time

• Philosophical centre of the realm.
• Macroscopic thermo gives time a direction.
• Hot coffee cools, gas spreads (doesn't reverse).

NODE 31

Entropy Phase Chg

ΔS=Q_rev/T

• Reversible transition at constant temp.
• ΔS_fus = L_fus / T.
• Connects to Realm 10 latent heat.

NODE 32

Entropy of Mixing

• Mixing, diffusion increases accessible micro-arrangements.
• Irreversibility. Connects to Molecular view.

NODE 33

Micro View Entropy

S=klnΩ

• k = Boltzmann const. Ω = micro-configurations.
• Bridge: Macro thermodynamics ↔ Micro statistical physics.

NODE 34

Free Expansion

• Gas expands into vacuum. Q=0, W=0, so ΔU=0.
• For ideal gas: ΔT=0, but Entropy INCREASES.
• ΔU=0 does NOT imply reversible or ΔS=0.

NODE 35

Heat Death

• Theoretical cosmological scenario.
• Universe approaches thermal equilibrium.
• Usable free-energy differences become limited.

NODE 36

Thermo Cycles

• Carnot, Otto, Diesel, Brayton, Rankine.
• Idealized engineering cycles.

NODE 37

Internal Combustion

• Intake → Compression → Combustion → Exhaust.
• Otto cycle vs Diesel cycle.
• Heat → Pressure → Work.

NODE 38

Steam Power

• Water → Steam → Expansion → Turbine.
• Rankine-cycle idea. Bridges thermo to electricity.

NODE 39

Thermo Potentials

H = U+PVF = U-TSG = H-TS

• Enthalpy (H), Helmholtz (F), Gibbs (G).
• Important for chemistry and materials.

NODE 40

Equations of State

REALGASES

• Beyond ideal gas: Deviations, interactions.
• Critical point, Phase diagram.

NODE 41

Phase Diagram

• Solid, Liquid, Gas boundaries.
• Triple point, Critical point.
• Connects to Realm 10.

NODE 42

Earth Thermo

• Atmosphere, weather, ocean circulation.
• Greenhouse effect, Earth's energy balance.

NODE 43

Life Thermo

• Metabolism, energy conversion, heat generation.
• Biological systems as open systems.

NODE 44

Tech Thermo

❄️⚙️🏭

• Engines, turbines, AC, power stations.
• Thermodynamics is a foundation of civilization.

NODE 45

Graph Chamber

• P-V, T-S, P-T diagrams.
• Area, state, path, cycle, direction.

NODE 46

Experiment Lab

P-T

Q

W

S

• Gas laws, specific heat, engine efficiency.
• SYS → STATE → PROCESS → MEASURE → ENERGY ACCT.

NODE 47

Misconceptions

• "Entropy = just disorder" → No.
• "Fridge creates cold" → Transfers heat via work.
• "Adiabatic = constant temp" → No, Q=0, T can change.

NODE 48

Solving Engine

• System? States? Changes? Q/W?
• 1st Law. Reversible? 2nd Law/Entropy.
• Cyclic → Engine/Fridge analysis.

NODE 49

Master Map

STATE → HEAT/WORK → ΔU1ST LAW → PROCESSES2ND LAW → ENTROPY → ENGINES

• The entire realm compressed.

NODE 50

Deep Synthesis

• 1st Law: Energy Accounting.
• 2nd Law: Direction & Limitations.
• Entropy gives the language connecting the two.