Chapter Introduction
Thermodynamics is the branch of physical chemistry that deals with energy transformations in chemical and physical processes. In CBSE Class 11 Chemistry, Chapter 6 introduces you to the laws governing heat, work, and energy — concepts that form the backbone of physical chemistry and are essential for NEET and JEE preparation.
This chapter connects the macroscopic properties of systems (temperature, pressure, volume) to energy changes. You will learn to predict whether a reaction will occur spontaneously using enthalpy, entropy, and Gibbs energy.
Key Definitions
| Term | Definition |
|---|---|
| System | The part of the universe under investigation (e.g., the reaction mixture in a beaker) |
| Surroundings | Everything outside the system |
| Boundary | The real or imaginary surface separating the system from the surroundings |
| State function | A property that depends only on the initial and final states, not on the path (e.g., U, H, S, G, T, P, V) |
| Path function | A property that depends on the path taken between states (e.g., heat q, work w) |
| Internal energy (U) | The total energy (kinetic + potential) of all molecules in the system; a state function |
| Enthalpy (H) | H = U + PV; heat content at constant pressure |
| Entropy (S) | A measure of disorder or randomness; ΔS = qrev / T |
| Gibbs energy (G) | G = H − TS; the thermodynamic potential used to predict spontaneity at constant T and P |
| Heat capacity | Amount of heat required to raise the temperature by 1 °C; C = q / ΔT |
System Types — Comparison
| Property | Open System | Closed System | Isolated System |
|---|---|---|---|
| Matter exchange | Yes | No | No |
| Energy exchange | Yes | Yes | No |
| Example | Open beaker | Sealed flask with movable piston | Thermos flask (ideal) |
| Boundary | Permeable | Impermeable to matter | Impermeable to both |
State Functions vs Path Functions
| State Functions | Path Functions |
|---|---|
| Internal energy (U) | Heat (q) |
| Enthalpy (H) | Work (w) |
| Entropy (S) | |
| Gibbs energy (G) | |
| Temperature, Pressure, Volume |
Key point: In a cyclic process, ΔU = 0, ΔH = 0, ΔS = 0, but q and w are generally non-zero.
Internal Energy and Work
Internal Energy (U)
- Sum of kinetic energy (translational, rotational, vibrational) and potential energy (intermolecular forces) of all particles.
- An extensive property (depends on amount of substance).
- For an ideal gas, U depends only on temperature.
PV Work (Expansion Work)
Work done by the system during expansion against external pressure:
w = −Pex × ΔV (constant external pressure)
For reversible isothermal expansion of an ideal gas:
w = −nRT ln(V₂/V₁) = −nRT ln(P₁/P₂)
Sign convention (IUPAC):
- Work done by the system is negative (w < 0)
- Work done on the system is positive (w > 0)
- Heat absorbed by the system is positive (q > 0)
- Heat released by the system is negative (q < 0)
The First Law of Thermodynamics
ΔU = q + w
Energy can neither be created nor destroyed; it can only be converted from one form to another.
| Condition | Equation | Meaning |
|---|---|---|
| At constant volume | w = 0 (no PV work) | ΔU = qv |
| At constant pressure | qp = ΔH | Heat absorbed = change in enthalpy |
| Cyclic process | ΔU = 0 | q = −w |
Enthalpy (H)
H = U + PV
At constant pressure: ΔH = ΔU + PΔV = ΔU + Δn(g)RT
Where Δn(g) = moles of gaseous products − moles of gaseous reactants.
| Δn(g) | Relationship | Example |
|---|---|---|
| = 0 | ΔH = ΔU | H₂(g) + Cl₂(g) → 2HCl(g) |
| > 0 | ΔH > ΔU | N₂(g) + O₂(g) → 2NO(g) |
| < 0 | ΔH < ΔU | 2SO₂(g) + O₂(g) → 2SO₃(g) |
Heat Capacity
| Property | Molar Heat Capacity | Relation |
|---|---|---|
| At constant pressure | Cp = qp / (nΔT) | Cp = Cv + R (for ideal gas) |
| At constant volume | Cv = qv / (nΔT) | Cv = (3/2)R for monatomic ideal gas |
| Cp − Cv | Cp − Cv = R | For 1 mole of ideal gas |
| Ratio | γ = Cp / Cv | γ = 5/3 for monatomic, 7/5 for diatomic |
For n moles: qp = nCpΔT and qv = nCvΔT
Standard Enthalpy of Reactions
| Type | Symbol | Definition |
|---|---|---|
| Standard enthalpy of formation | ΔfH° | Enthalpy change when 1 mole of a compound forms from its elements in standard states |
| Standard enthalpy of combustion | ΔcH° | Enthalpy change when 1 mole of a substance is completely burnt in oxygen |
| Enthalpy of atomization | ΔaH° | Enthalpy change to break 1 mole of a substance into gaseous atoms |
| Bond enthalpy | ΔbondH° | Average enthalpy change to break 1 mole of a particular bond in gaseous state |
| Enthalpy of solution | ΔsolH° | Enthalpy change when 1 mole of solute dissolves in a solvent |
| Enthalpy of fusion | ΔfusH° | Enthalpy change for melting 1 mole of solid to liquid |
| Enthalpy of vaporization | ΔvapH° | Enthalpy change for vaporizing 1 mole of liquid to gas |
| Lattice enthalpy | ΔlatticeH° | Enthalpy change when 1 mole of ionic compound separates into gaseous ions |
Hess's Law of Constant Heat Summation
The total enthalpy change for a reaction is the same whether it takes place in one step or in multiple steps.
Applications: 1. Calculate ΔH for reactions that cannot be measured directly. 2. Calculate ΔfH using known enthalpies of combustion. 3. Calculate lattice enthalpy using Born-Haber cycle.
Example: To find ΔH for C(s) + ½O₂(g) → CO(g):
- C(s) + O₂(g) → CO₂(g); ΔH = −393.5 kJ/mol
- CO(g) + ½O₂(g) → CO₂(g); ΔH = −283.0 kJ/mol
- Subtracting: C(s) + ½O₂(g) → CO(g); ΔH = −110.5 kJ/mol
Entropy (S)
Second Law of Thermodynamics
In any spontaneous process, the total entropy of the system and surroundings always increases.
For a reversible process: ΔS = qrev / T
For an irreversible process: ΔStotal > 0
| Process | ΔS |
|---|---|
| Melting of ice | Positive (solid → liquid) |
| Vaporization | Positive (liquid → gas) |
| Expansion of gas | Positive |
| Crystallization | Negative (gas/liquid → solid) |
Standard entropy change for a reaction:
ΔrS° = ΣS°(products) − ΣS°(reactants)
Gibbs Energy and Spontaneity
ΔG = ΔH − TΔS (at constant temperature and pressure)
| ΔH | ΔS | Condition | Spontaneity | ||||
|---|---|---|---|---|---|---|---|
| −ve | +ve | All temperatures | Always spontaneous | ||||
| +ve | −ve | All temperatures | Always non-spontaneous | ||||
| −ve | −ve | Low T ( | ΔH | > | TΔS | ) | Spontaneous at low T |
| +ve | +ve | High T ( | TΔS | > | ΔH | ) | Spontaneous at high T |
At equilibrium: ΔG = 0, so ΔH = TΔS → T = ΔH / ΔS
Third Law of Thermodynamics
The entropy of a perfectly crystalline substance is zero at absolute zero (0 K).
This law provides a reference point for calculating absolute entropies: S° at 298 K for any substance can be determined.
Important Numerical Patterns
Pattern 1: Calculating ΔU from q and w
If 500 J of heat is supplied to a system and the system does 200 J of work on the surroundings:
- q = +500 J (heat absorbed), w = −200 J (work done by system)
- ΔU = q + w = 500 + (−200) = +300 J
Pattern 2: Calculating ΔH from ΔU
For the reaction N₂(g) + 3H₂(g) → 2NH₃(g) at 298 K, if ΔU = −87.42 kJ/mol:
- Δn(g) = 2 − (1 + 3) = 2 − 4 = −2
- ΔH = ΔU + Δn(g)RT = −87.42 + (−2)(8.314 × 10⁻³)(298) = −87.42 − 4.96 = −92.38 kJ/mol
Pattern 3: Hess's Law — Born-Haber Cycle for NaCl
- ΔfH°(NaCl) = ΔsubH°(Na) + ΔionH°(Na) + ½ΔbondH°(Cl₂) + ΔegH°(Cl) + ΔlatticeH°(NaCl)
- Use this to calculate lattice enthalpy when other values are known.
Pattern 4: Spontaneity from ΔG
For a reaction with ΔH = +80 kJ/mol and ΔS = +150 J/(mol·K) at 400 K:
- ΔG = ΔH − TΔS = 80000 − 400 × 150 = 80000 − 60000 = +20000 J/mol = +20 kJ/mol
- ΔG > 0, so the reaction is non-spontaneous at 400 K.
- It becomes spontaneous when T > ΔH/ΔS = 80000/150 = 533.3 K.
Pattern 5: Entropy change
For melting of ice at 273 K (ΔfusH = 6.0 kJ/mol):
- ΔS = ΔH / T = 6000 / 273 = 21.98 J/(mol·K)
Common Mistakes
1. Confusing sign conventions: Remember IUPAC — work done BY the system is negative, heat absorbed BY the system is positive. Many students reverse these.
2. Using ΔH = ΔU + ΔnRT instead of Δn(g)RT: Only count gaseous moles, not all moles. Solids and liquids contribute negligibly to volume change.
3. Forgetting to convert units: ΔS is usually in J/(mol·K), but ΔH is in kJ/mol. Always convert to the same unit before using ΔG = ΔH − TΔS.
4. Assuming ΔH = ΔU always: They are equal only when Δn(g) = 0 (equal moles of gas on both sides).
5. Confusing Cp and Cv: Cp is at constant pressure, Cv at constant volume. For an ideal gas, Cp − Cv = R. Using Cv when constant pressure conditions apply gives wrong answers.
6. Hess's law errors: When manipulating equations, reverse the sign of ΔH when you reverse the equation; multiply ΔH by the same factor when you multiply the equation.
7. Spontaneity confusion: ΔS(system) > 0 does NOT guarantee spontaneity. You must consider the total entropy change (system + surroundings) or use ΔG.
Exam Tips
1. One-mark answers: Memorize definitions of state function, path function, isolated system, entropy, and Gibbs energy. These appear frequently.
2. Numericals: Practice ΔU, ΔH, and ΔG calculations. At least one numerical is almost guaranteed. Always show: formula → substitution → answer with unit.
3. Hess's law: A 3-mark or 5-mark question is very likely. Practice Born-Haber cycle construction for NaCl, MgCl₂.
4. Spontaneity table: The ΔH/ΔS/T table is a frequent 2-mark question. Write the four combinations clearly.
5. Third law: Be ready to explain why entropy is zero at 0 K for a perfect crystal — a common short-answer question.
6. Relation questions: "Derive ΔH = ΔU + Δn(g)RT" and "Show that Cp − Cv = R" are frequent derivations.
7. Graph-based questions: Isothermal and adiabatic PV diagrams can appear. Know the shapes: isothermal is flatter than adiabatic.
Quick Revision Notes
- First law: ΔU = q + w. Energy is conserved.
- Enthalpy: H = U + PV; ΔH = qp (heat at constant pressure).
- ΔH and ΔU: ΔH = ΔU + Δn(g)RT. Equal when Δn(g) = 0.
- Cp − Cv = R for 1 mole of ideal gas.
- Standard formation: ΔfH° of an element in its standard state = 0.
- Hess's law: ΔH is path-independent; add ΔH values algebraically.
- Second law: Total entropy increases for spontaneous processes.
- ΔS = qrev / T (reversible process).
- ΔG = ΔH − TΔS. Spontaneous if ΔG < 0.
- At equilibrium: ΔG = 0, T = ΔH/ΔS.
- Third law: S → 0 as T → 0 K for a perfect crystal.
- Work: w = −PexΔV (irreversible); w = −nRT ln(V₂/V₁) (reversible isothermal).
- Bond enthalpy is average value; differs from bond dissociation enthalpy for polyatomic molecules.
- Spontaneity shortcut: −ve ΔH and +ve ΔS → always spontaneous; +ve ΔH and −ve ΔS → never spontaneous.
NCERT Exercise Focus Areas
The following NCERT exercise question types are most likely to appear in exams. Prioritize these during revision:
| Question Type | Chapter Examples | Marks |
|---|---|---|
| Define and distinguish (state vs path function) | Q1, Q2 | 1–2 |
| Calculate ΔU, q, w from given data | Q6, Q7 | 2–3 |
| Derive ΔH = ΔU + Δn(g)RT | Q8 | 3 |
| Calculate ΔH using Hess's law | Q12, Q13 | 3–5 |
| Spontaneity prediction using ΔG | Q16, Q17 | 2–3 |
| Entropy change calculations | Q14, Q15 | 2–3 |
| Born-Haber cycle construction | Q11 | 5 |
Derivations to Master
1. Relationship between ΔH and ΔU
From the definition of enthalpy: H = U + PV
For a process: ΔH = ΔU + Δ(PV)
At constant pressure: ΔH = ΔU + PΔV
For ideal gas: PV = nRT, so PΔV = Δn(g)RT
2. Cp − Cv = R (Mayer's relation)
At constant pressure: qp = nCpΔT = ΔH
At constant volume: qv = nCvΔT = ΔU
From first law: qp − qv = ΔH − ΔU = PΔV = P × nRΔT/P = nRΔT
Dividing by nΔT: Cp − Cv = R
3. Work done in isothermal reversible expansion
w = −∫PexdV = −∫(nRT/V)dV (since PV = nRT for ideal gas)
w = −nRT ln(V₂/V₁) = −nRT × 2.303 × log(V₂/V₁) = −2.303 nRT log(V₂/V₁)
Since P₁V₁ = P₂V₂ for isothermal process: w = −nRT ln(P₁/P₂)
