Thermodynamics & Thermochemistry – Complete Short Notes

1. Thermodynamics – Introduction & Basic Terminology

Introduction

Thermodynamics: Branch of science which studies motion of thermal energy from one place to another.
Thermo = Thermal energy (heat) | Dynamic = Movement

Two Branches:
• Classical Thermodynamics → Macroscopic objects (bulk properties)
• Statistical Thermodynamics → Microscopic objects (individual molecules)

Basic Terminology

Universe: Total available space. Universe = System + Surrounding
System: Part of universe under study (substance/reaction under consideration)
Surrounding: Everything in universe except the system
Boundary: Surface separating system and surrounding (can be real or imaginary)
Extensive Properties: Depend on amount of matter — mass, volume, internal energy, enthalpy, entropy, heat capacity
Intensive Properties: Independent of amount — temperature, pressure, density, viscosity, refractive index, surface tension, specific heat, molar properties

📝 Ratio of two extensive properties gives an intensive property. E.g., mass/volume = density (intensive)

2. Types of Systems & Thermodynamic Processes

Types of Systems

System	Matter Exchange	Energy Exchange	Example
Open	Yes	Yes	Open beaker, human body
Closed	No	Yes	Closed steel vessel
Isolated	No	No	Thermos flask (ideal)

Types of Processes

Process	Condition	Key Relation
Isothermal	T = constant (dT = 0)	ΔU = 0 (ideal gas); q = –w
Adiabatic	q = 0 (no heat exchange)	ΔU = w
Isobaric	P = constant (dP = 0)	q = ΔH
Isochoric	V = constant (dV = 0)	w = 0; q = ΔU
Cyclic	System returns to initial state	ΔU = 0; ΔH = 0; q = –w

Reversible Process: System and surrounding in equilibrium at every step; infinitely slow; theoretical maximum work

Irreversible Process: Spontaneous; fast; practically carried out; gives less work than reversible

Work Done (w)

Expansion work (PV work): w = –P_extΔV = –P_ext(V₂ – V₁)
For free expansion: P_ext = 0, so w = 0
For reversible isothermal expansion (ideal gas):

w = –nRT ln(V₂/V₁) = –nRT ln(P₁/P₂) = –2.303 nRT log(V₂/V₁)

📝 Sign convention: Work done BY system = negative (–w). Work done ON system = positive (+w). IUPAC convention: w = –P_extΔV

3. State Functions & Path Functions

State Functions

Depend only on initial and final state, NOT on path taken
Examples: T, P, V, U, H, S, G — all thermodynamic properties
Change denoted by Δ (delta): ΔU, ΔH, ΔS, ΔG

Path Functions

Depend on the path taken between two states
Examples: Heat (q) and Work (w)
NOT state functions — cannot write Δq or Δw

🔴 Important: q and w are NOT state functions but (q + w) = ΔU IS a state function

Thermodynamic Equilibrium

System is in thermodynamic equilibrium when: Thermal equilibrium (uniform T) + Mechanical equilibrium (uniform P) + Chemical equilibrium (no composition change)
State of system fully described by T, P, V, n

4. Internal Energy & First Law of Thermodynamics (FLOT)

Internal Energy (U)

Total energy stored in a system (kinetic + potential energy of all molecules)
Extensive property, state function
Absolute value cannot be measured; only ΔU can be measured
For ideal gas: U depends only on temperature (not on P or V)

ΔU = U_final – U_initial
ΔU > 0 → endothermic (system absorbs energy)
ΔU < 0 → exothermic (system releases energy)

First Law of Thermodynamics (FLOT)

Statement: Energy can neither be created nor destroyed, only converted from one form to another. Total energy of universe is constant.
Also called: Law of Conservation of Energy

Mathematical Form:
ΔU = q + w (IUPAC convention)

Where: q = heat absorbed by system (+ve if absorbed, –ve if released)
w = work done on system (+ve if done on, –ve if done by system)
w = –P_extΔV

📝 Old convention: ΔU = q – w (work done BY system positive). IUPAC: ΔU = q + w (work done ON system positive). Always check which convention is used!

FLOT for Different Processes

Process	Condition	FLOT Result
Isothermal (ideal gas)	ΔU = 0, dT = 0	q = –w
Adiabatic	q = 0	ΔU = w
Isochoric	ΔV = 0, w = 0	ΔU = q_v
Free Expansion	P_ext = 0, q = 0	ΔU = 0

Relation Between q_p and q_v

q_p = q_v + Δn_gRT

Where Δn_g = moles of gaseous products – moles of gaseous reactants
q_p = heat at constant pressure = ΔH
q_v = heat at constant volume = ΔU

🔴 This relation is very important for converting bomb calorimeter data (q_v) to ΔH (q_p)

5. Enthalpy (H) & Heat Capacity

Enthalpy (H)

H = U + PV (thermodynamic function, state function, extensive)
At constant pressure: ΔH = ΔU + PΔV = ΔU + Δn_gRT
For reactions involving only liquids/solids: ΔV ≈ 0, so ΔH ≈ ΔU
ΔH = q_p (heat absorbed at constant pressure)

ΔH = H_products – H_reactants
ΔH < 0 → Exothermic reaction (heat released)
ΔH > 0 → Endothermic reaction (heat absorbed)

Heat Capacity

Heat Capacity (C): Heat required to raise temperature of substance by 1 K/1°C
Specific Heat Capacity (c or s): Heat required to raise temperature of 1 g by 1 K
Molar Heat Capacity (C_m): Heat required to raise temperature of 1 mole by 1 K

q = mcΔT = nC_mΔT

C_p – C_v = R (for ideal gas)
C_p/C_v = γ (ratio of heat capacities)

For monoatomic gas: C_v = 3/2 R, C_p = 5/2 R, γ = 5/3
For diatomic gas: C_v = 5/2 R, C_p = 7/2 R, γ = 7/5

Calorimetry

Coffee Cup Calorimeter: Constant pressure calorimeter; measures ΔH directly; q = mcΔT
Bomb Calorimeter: Constant volume calorimeter; measures ΔU; then convert to ΔH using ΔH = ΔU + Δn_gRT

For Bomb Calorimeter: q_v = C_cal × ΔT
C_cal = heat capacity of calorimeter (kJ/K)

6. Thermochemistry – Types of Enthalpy Changes

Standard Enthalpy of Formation (ΔH°f)

Enthalpy change when 1 mole of compound is formed from its elements in their standard states
Standard state: Pure substance at 1 bar pressure (and specified temperature, usually 298 K)
ΔH°f of elements in standard state = 0 (by definition)

ΔH°_reaction = Σ ΔH°f (products) – Σ ΔH°f (reactants)

Enthalpy of Combustion (ΔH°c)

Enthalpy change when 1 mole of substance is completely burnt in excess oxygen at standard conditions
Always exothermic (negative) for organic compounds
Used to calculate calorific value of fuels

C(s) + O₂(g) → CO₂(g) ΔH°c = –393.5 kJ/mol
H₂(g) + ½O₂(g) → H₂O(l) ΔH°c = –285.8 kJ/mol

Enthalpy of Neutralization

Enthalpy change when 1 mole of water is formed by neutralization of acid with base
Strong acid + Strong base: Always –57.1 kJ/mol (enthalpy of ionic reaction H⁺ + OH⁻ → H₂O)
Weak acid or weak base involved: Less than –57.1 kJ/mol (energy required for ionization)

Heat of ionization = 57.1 – |observed neutralization enthalpy|

HCN + NaOH: ΔH = –12.1 kJ/mol → Heat of ionization of HCN = 57.1 – 12.1 = 45 kJ/mol

Enthalpy of Solution & Hydration

Enthalpy of Solution: ΔH when 1 mole solute dissolves in excess solvent
Enthalpy of Hydration: ΔH when 1 mole of anhydrous salt combines with water to form hydrate
Lattice Energy (U): Energy required to separate 1 mole of ionic compound into gaseous ions (endothermic)

ΔH_solution = Lattice Energy + ΔH_hydration

Enthalpy of Atomization & Sublimation

Atomization: ΔH to convert 1 mole of substance into gaseous atoms; always endothermic
Sublimation: ΔH for solid → gas conversion
For diatomic molecules: ΔH_atomization = Bond Dissociation Energy / 2 × 2 (per mole atoms)
Vaporization (ΔH_vap): Liquid → Gas; endothermic
Fusion (ΔH_fus): Solid → Liquid; endothermic

Born-Haber Cycle

Thermochemical cycle to calculate lattice energy of ionic compounds
Uses Hess's law; relates formation enthalpy to all intermediate steps

For NaCl formation:
ΔH°f = ΔH_sub(Na) + IE(Na) + ½ΔH_diss(Cl₂) + EA(Cl) + U(NaCl)

Where: sub = sublimation, IE = ionization energy, diss = dissociation, EA = electron affinity, U = lattice energy

7. Hess's Law & Kirchhoff's Law

Hess's Law of Constant Heat Summation

Statement: Total enthalpy change of a reaction is the same regardless of whether reaction occurs in one step or multiple steps, as long as initial and final states are same.
Consequence of H being a state function
Allows calculation of ΔH for reactions that cannot be carried out directly

If reaction A → C can be written as:
A → B : ΔH₁
B → C : ΔH₂
Then A → C : ΔH = ΔH₁ + ΔH₂

📝 When a reaction is reversed, sign of ΔH changes. When multiplied by n, ΔH also multiplies by n.

Applications of Hess's Law

Calculating ΔH°f for compounds that cannot be directly synthesized
Calculating bond energies from experimental thermochemical data
Calculating ΔH of transition between allotropic forms
Calculating lattice energy via Born-Haber cycle

ΔH°_rxn = Σ ΔH°f (products) – Σ ΔH°f (reactants)

ΔH°_rxn = Σ BE (reactants) – Σ BE (products) [using bond energies]

Kirchhoff's Law (Temperature Dependence of ΔH)

ΔH(T₂) = ΔH(T₁) + ΔC_p(T₂ – T₁)

Where ΔC_p = Σ C_p(products) – Σ C_p(reactants)

Similarly: ΔU(T₂) = ΔU(T₁) + ΔC_v(T₂ – T₁)

8. Bond Energy & Resonance Energy

Bond Dissociation Energy (BDE)

Energy required to break 1 mole of a specific bond in gaseous molecules into gaseous atoms/radicals
Always endothermic (positive value)
For diatomic molecules: BDE = bond energy (unique, exact value)
For polyatomic molecules: BDE varies for each successive bond broken

Mean Bond Energy

Average energy required to break all bonds of same type in polyatomic molecule
Used for polyatomic molecules (e.g., O–H in H₂O: 498/2 = 249 kJ/mol per bond)

ΔH°_rxn = Σ Bond Energies (broken/reactants) – Σ Bond Energies (formed/products)

Remember: Bond breaking = endothermic (+ve) | Bond forming = exothermic (–ve)

Resonance Energy

Difference between actual enthalpy and theoretical enthalpy calculated from bond energies
Shows extra stability due to delocalization of electrons

Resonance Energy = ΔH°f (theoretical/calculated) – ΔH°f (experimental)

For benzene: Resonance energy ≈ –152 kJ/mol (benzene is more stable than expected)

Important Bond Energy Values

Bond	Bond Energy (kJ/mol)
H–H	436
C–C	347
C=C	611
C≡C	837
C–H	414
O–H	460 (BDE); 498/2=249 (mean)
O=O	498
N≡N	945
C=O (CO₂)	799

9. Second Law of Thermodynamics & Entropy (S)

Second Law of Thermodynamics (SLOT)

Kelvin-Planck Statement: It is impossible to construct a heat engine that converts heat completely into work in a cyclic process.
Clausius Statement: Heat cannot flow spontaneously from cold body to hot body without external work.
Entropy Statement: Total entropy of universe always increases for spontaneous processes (ΔS_universe > 0)

Entropy (S)

Measure of disorder or randomness in a system
State function, extensive property
S increases as: solid < liquid < gas; fewer moles < more moles of gas; lower T < higher T
Units: J/K/mol or J K⁻¹ mol⁻¹

ΔS = q_rev/T (at constant temperature)

ΔS = nC_v ln(T₂/T₁) + nR ln(V₂/V₁) [for ideal gas, general]

ΔS = nC_p ln(T₂/T₁) – nR ln(P₂/P₁) [for ideal gas, general]

For isothermal expansion: ΔS = nR ln(V₂/V₁) = 2.303 nR log(V₂/V₁)

Entropy & Spontaneity

ΔS_universe = ΔS_system + ΔS_surrounding
Spontaneous: ΔS_universe > 0
At equilibrium: ΔS_universe = 0
Non-spontaneous: ΔS_universe < 0

ΔS_surrounding = –ΔH_system/T (at constant T and P)

ΔS_universe = ΔS_sys – ΔH_sys/T > 0 (for spontaneous process)

Boltzmann Entropy

S = k_B ln W

Where k_B = Boltzmann constant = 1.38 × 10⁻²³ J/K
W = number of microstates (thermodynamic probability)

10. Gibbs Free Energy (G) & Spontaneity

Gibbs Free Energy

G = H – TS (Gibbs-Helmholtz equation)
State function, extensive property
Combines enthalpy and entropy into one criterion for spontaneity at constant T and P

ΔG = ΔH – TΔS (at constant T and P)

ΔG < 0 → Spontaneous (feasible)
ΔG = 0 → At equilibrium
ΔG > 0 → Non-spontaneous (reverse is spontaneous)

Spontaneity Analysis (ΔH and ΔS combinations)

ΔH	ΔS	ΔG = ΔH – TΔS	Spontaneity
– (exo)	+ (increase)	Always –ve	Always spontaneous ✓
+ (endo)	– (decrease)	Always +ve	Never spontaneous ✗
– (exo)	– (decrease)	–ve at low T	Spontaneous at low T
+ (endo)	+ (increase)	–ve at high T	Spontaneous at high T

🔴 Crossover Temperature: T = ΔH/ΔS (where ΔG = 0, process just becomes spontaneous/non-spontaneous)

ΔG and Equilibrium

ΔG° = –RT ln K_eq = –2.303 RT log K_eq

ΔG = ΔG° + RT ln Q

At equilibrium: Q = K, ΔG = 0
ΔG° = –RT ln K

K value	ΔG°	Meaning
K > 1	ΔG° < 0	Products favored
K = 1	ΔG° = 0	Equal tendency
K < 1	ΔG° > 0	Reactants favored

Maximum Work & ΔG

–ΔG = w_max (maximum non-expansion work obtainable from process)

For electrochemical cells: ΔG = –nFE_cell
ΔG° = –nFE°_cell

11. Third Law of Thermodynamics & Important Values

Third Law of Thermodynamics

Statement: Entropy of a perfect crystalline substance at absolute zero (0 K) is zero.
Allows calculation of absolute entropy values (unlike H and U, absolute S can be determined)
S° at 298 K values are tabulated — always positive for real substances

S(0 K) = 0 for perfect crystal

ΔS°_rxn = Σ S° (products) – Σ S° (reactants)

Standard Entropy Values (S°) at 298 K

Substance	S° (J/K/mol)
H₂(g)	130.7
O₂(g)	205.1
H₂O(l)	70.0
H₂O(g)	188.7
CO₂(g)	213.7
C (graphite)	5.7
C (diamond)	2.4
NaCl(s)	72.1

Comparison: Graphite vs Diamond

Graphite is more stable than diamond under standard conditions (lower ΔG°f)
S°(graphite) > S°(diamond) → graphite has more disorder
Conversion of diamond to graphite: spontaneous but extremely slow kinetically

Trouton's Rule

ΔS_vap ≈ 88 J/K/mol for most liquids (at boiling point)

ΔS_vap = ΔH_vap / T_b

📝 Exceptions: Water, alcohols, other H-bonded liquids have ΔS_vap > 88 due to ordered liquid structure.

12. Complete Formula Summary

All Key Equations at a Glance

FLOT: ΔU = q + w | w = –P_extΔV

Reversible isothermal work: w = –nRT ln(V₂/V₁)

Enthalpy: H = U + PV | ΔH = ΔU + Δn_gRT

Heat: q = mcΔT = nC_mΔT

Hess's Law: ΔH°_rxn = Σ ΔH°f(P) – Σ ΔH°f(R)

Bond Energy: ΔH°_rxn = Σ BE(reactants) – Σ BE(products)

Kirchhoff's Law: ΔH(T₂) = ΔH(T₁) + ΔC_p(T₂ – T₁)

Entropy: ΔS = q_rev/T | S = k_B ln W

Entropy (isothermal ideal gas): ΔS = nR ln(V₂/V₁)

Gibbs Energy: G = H – TS | ΔG = ΔH – TΔS

ΔG & K: ΔG° = –RT ln K = –2.303 RT log K

ΔG & Q: ΔG = ΔG° + RT ln Q

Max work: –ΔG = w_max

Electrochemistry link: ΔG = –nFE_cell

Neutralization: Strong acid + Strong base → ΔH = –57.1 kJ/mol

C_p – C_v = R (ideal gas)

Quick Memory Aid – SLOT Spontaneity

Spontaneous if: ΔS_universe > 0 OR ΔG_system < 0 (at const. T, P)

Both conditions are equivalent and can be derived from each other