Thermodynamics

2.1 Core concepts

• System and surroundings. System = part of universe under observation; surroundings = remaining universe that can interact with it; the wall between them is the boundary, real or imaginary (NCERT §5.1.1, p. 137).
• Types of system. Open = exchanges both matter and energy (open beaker); closed = exchanges only energy (sealed copper vessel); isolated = exchanges neither (thermos flask) (NCERT §5.1.2, p. 137–138).
• State of a system. Specified by state variables p, V, T, n; once a minimum set is fixed, all other macroscopic properties follow. State functions depend only on present state, not on path taken (NCERT §5.1.3, p. 138). The minimum set is independent of the choice of path used to reach that state.
• Internal energy U as state function. Sum of all forms of energy (chemical, mechanical, electrical, kinetic, potential, vibrational, rotational) of the system; can change by heat flow, work, or matter transfer. Joule's adiabatic experiments (1840–50) showed wad is path-independent, so ΔU = wad in an adiabatic process — a numerically equal amount of work whether performed mechanically, electrically or by friction (NCERT §5.1.4, p. 138–139).
• Sign convention (IUPAC). q positive when heat is absorbed by the system; w positive when work is done on the system; both negative when energy leaves the system. ΔU > 0 if the system gains energy and < 0 if it loses energy (NCERT §5.1.4, p. 139).
• First law of thermodynamics. ΔU = q + w; energy of an isolated system is constant (q = 0, w = 0 ⇒ ΔU = 0). Energy can neither be created nor destroyed, only converted from one form to another (NCERT §5.1.4(c), p. 140, Eq. 5.1).
• Pressure–volume work. w = −pext ΔV for a single-step (irreversible) compression; for reversible isothermal expansion of an ideal gas, wrev = −2.303 nRT log(V₂/V₁). The reversible work is the maximum work the gas can deliver because pext is set infinitesimally lower than pin at every step (NCERT §5.2.1, p. 140–142, Eq. 5.2 & 5.5).
• Free expansion. pext = 0, so w = 0; for an isothermal ideal-gas free expansion ΔU = 0 (no temperature change) and q = 0 too (NCERT §5.2.1, p. 142).
• Special cases. Constant volume: ΔU = qV (because w = 0). Adiabatic: q = 0, so ΔU = wad. Constant pressure: ΔH = qp (NCERT §5.2.1, p. 142).
• Enthalpy. H = U + pV is a state function; at constant pressure ΔH = qp = heat absorbed. ΔH = ΔU + Δng RT relates enthalpy and internal energy for gas-phase reactions; Δng = moles of gaseous products − moles of gaseous reactants (NCERT §5.2.2(a), p. 143, Eq. 5.7 & 5.10). For solids/liquids, ΔH ≈ ΔU because pΔV is negligible.
• Extensive vs intensive. Extensive properties (mass, V, U, H, S, heat capacity) depend on amount; intensive properties (T, p, density, molar quantities, viscosity, refractive index) do not. Ratios of two extensive properties (density = m/V; molar volume V/n) are intensive (NCERT §5.2.2(b), p. 144).
• Heat capacity. q = C ΔT; molar heat capacity Cm = C/n; specific heat c = q/(m ΔT). For an ideal gas, Cp − Cv = R; the extra heat at constant pressure goes into pV expansion work. For monatomic ideal gas Cv = (3/2)R, Cp = (5/2)R, γ = 5/3 (NCERT §5.2.2(c–d), p. 144–145, Eq. 5.13).
• Calorimetry. ΔU measured in a constant-volume bomb calorimeter (no work because ΔV = 0; heat evolved heats the steel bomb + water bath); ΔH measured in a constant-pressure (coffee-cup) calorimeter, where qp = ΔrH. Calorimeter constant must be known from a calibration run (NCERT §5.3, p. 145–146).
• Reaction enthalpy and standard states. ΔrH = Σai Hproducts − Σbi Hreactants. Standard state of a substance = its pure form at 1 bar (and usually 298 K); denoted by superscript °. For solutes, standard state is hypothetical 1 mol kg⁻¹ ideal solution (NCERT §5.4(a), p. 146–147, Eq. 5.14).
• Phase-change enthalpies. ΔfusH° (always positive, e.g., ice → water +6.00 kJ/mol at 273 K), ΔvapH° (water → steam +40.79 kJ/mol at 373 K), ΔsubH° (always positive) — all measured per mole at constant T and p (NCERT §5.4(b), p. 147–148).
• Standard enthalpy of formation, ΔfH°. Enthalpy change when 1 mol of a compound forms from its elements in their reference (most stable) states at 1 bar and 298 K. ΔfH° of an element in its reference state = 0 by convention (NCERT §5.4(c), p. 149–150, Eq. 5.15).
• Thermochemical equations. Must specify physical state; coefficients refer to moles; reversing the equation reverses the sign of ΔrH; multiplying by a factor multiplies ΔrH by the same factor (NCERT §5.4(d), p. 150–151).
• Hess's law of constant heat summation. Total ΔrH for a reaction is the sum of ΔrH of the steps into which it can be divided; allows indirect calculation of unmeasurable enthalpies, e.g. C + ½O₂ → CO via C → CO₂ and CO → CO₂ (NCERT §5.4(e), p. 151–152, Eq. 5.16). Direct measurement of C + ½O₂ → CO is impossible because some CO₂ always forms.
• Enthalpies of various reactions. Combustion ΔcH° (always exothermic, e.g. butane −2658, glucose −2802 kJ/mol); atomization ΔaH° (= bond dissociation enthalpy for diatomics); bond enthalpy ΔbondH°; mean bond enthalpy (e.g. ΔC–HH° = ¼·1665 = 416 kJ/mol in CH₄); ΔrH° = Σ bond enthalpies(reactants) − Σ bond enthalpies(products) for gas-phase reactions (NCERT §5.5(a–c), p. 152–155, Eq. 5.17).
• Lattice enthalpy and Born–Haber cycle. ΔlatticeH° = enthalpy change when 1 mol of ionic solid dissociates into gaseous ions; computed indirectly via Born–Haber cycle using sublimation + ionization + dissociation + electron-gain + lattice steps. ΔsolH° = ΔlatticeH° + ΔhydH° — most ionic solids dissolve in water because hydration enthalpy is exothermic and large enough to overcome lattice enthalpy (NCERT §5.5(d–e), p. 155–156).
• Spontaneity. A spontaneous process has the potential to proceed without external help; it is irreversible. Decrease in enthalpy is not a sufficient criterion — endothermic reactions like ½N₂ + O₂ → NO₂ (ΔrH = +33.2 kJ/mol) are also spontaneous. Mixing of two gases is spontaneous with ΔH ≈ 0 (NCERT §5.6 & §5.6(a), p. 157–158).
• Entropy S. A state function and measure of disorder/randomness; ΔS = qrev/T. Gaseous state has highest S, crystalline solid lowest. For a spontaneous process in an isolated system, ΔStotal = ΔSsys + ΔSsurr > 0; ΔStotal = 0 at equilibrium (NCERT §5.6(b), p. 158–159, Eq. 5.18 & 5.19).
• Gibbs energy. G = H − TS; at constant T, ΔG = ΔH − TΔS. ΔG < 0 ⇒ spontaneous; ΔG > 0 ⇒ non-spontaneous; ΔG = 0 ⇒ equilibrium. ΔG is the "free" (useful work) energy of the reaction; ΔG also equals the maximum non-pV work available from the system at constant T, p (NCERT §5.6(c), p. 160–161, Eq. 5.20 & 5.21).
• Second law of thermodynamics. Entropy of an isolated system increases for a spontaneous process; explains why exothermic reactions tend to be spontaneous (heat released raises Ssurr, ΔSsurr = −ΔHsys/T) (NCERT §5.6(d), p. 161).
• Third law of thermodynamics. Entropy of a pure crystalline substance approaches zero as T → 0 K; lets us calculate absolute entropies by integrating qrev/T from 0 K to T. Allows tabulation of standard absolute entropies S° at 298 K (NCERT §5.6(e), p. 161–162).
• ΔG° and equilibrium constant. At equilibrium ΔrG = 0; ΔrG° = −RT ln K = −2.303 RT log K. Large negative ΔrG° ⇒ K >> 1 (reaction near completion); large positive ⇒ K << 1; ΔrG° ≈ 0 ⇒ K ≈ 1 (NCERT §5.7, p. 162, Eq. 5.23).

2.2 Definitions to memorise

2.3 Diagrams / processes to remember

• Fig. 5.2 (p. 137): Open, closed and isolated systems — three labelled containers showing matter/energy exchange. Open beaker shows arrows for both matter (vapour) and heat; closed system shows only heat arrows through a sealed lid; isolated system (thermos) has neither.
• Fig. 5.5(a–c) (p. 140–141): pV-plots of work done — single-step (rectangle of area pext·ΔV), finite-step (staircase whose total area is the sum of rectangles), and infinite-step reversible (smooth hyperbola whose shaded area equals nRT ln(V₂/V₁), the maximum possible work). The diagrams visually illustrate why wrev > wirrev for expansion.
• Fig. 5.7 (p. 145): Bomb calorimeter — steel bomb in a water bath; constant-volume ΔU measurement. The bomb is filled with O₂ at high pressure, electrical ignition burns the sample, and the temperature rise of the surrounding water gives qV which equals ΔU directly. Used for combustion enthalpies of food, fuels.
• Fig. 5.8 (p. 146): Coffee-cup / constant-pressure calorimeter for ΔH measurement of dissolution and neutralisation reactions in aqueous solution. Polystyrene cup acts as adiabatic shield; measured qp = ΔH directly.
• Fig. 5.9 (p. 155): Born–Haber enthalpy diagram for NaCl — sublimation (+108.4 kJ/mol) + ionization (+496) + ½ bond dissociation (+121) + electron-gain (−348.6) + lattice (−788) = −411.2 kJ/mol formation enthalpy. The vertical-arrow construction shows how an indirect cycle gives the otherwise unmeasurable ΔlatticeH°.
• Fig. 5.10(a) & (b) (p. 158): Enthalpy diagrams for exothermic (products below reactants) and endothermic (products above reactants) reactions; the vertical arrow downwards/upwards represents −ΔH or +ΔH respectively.
• Fig. 5.11 (p. 158): Diffusion of two gases A and B before and after partition removal — visual for entropy increase. The number of accessible microstates rises sharply on mixing, so ΔS_mix > 0 even though ΔH_mix ≈ 0 for ideal gases.
• Table 5.4 (p. 162): Effect of ΔH, ΔS and T on the sign of ΔG (spontaneity matrix): ΔH<0, ΔS>0 → spontaneous at all T; ΔH>0, ΔS<0 → non-spontaneous at all T; ΔH<0, ΔS<0 → spontaneous at low T; ΔH>0, ΔS>0 → spontaneous at high T. A four-row table that summarises every spontaneity case.
• PE diagram of catalysed vs uncatalysed reaction (implicit, p. 158): identical reactants and products, but the activation barrier lowered by the catalyst; the overall ΔH (and ΔG) is unchanged because state functions depend only on initial/final states.

2.4 Common confusions / NTA trap points

• Sign convention. IUPAC: w is positive when work is done on the system. Older physics books use the opposite sign — NTA distractors exploit this. If the gas expands (V₂ > V₁), w < 0 (work done by gas).
• ΔH vs ΔU. They are equal only when Δng = 0 (no change in moles of gas) or for solids/liquids; otherwise ΔH = ΔU + Δng RT. For H₂(g) + ½O₂(g) → H₂O(l), Δng = −1.5, so ΔH < ΔU.
• q is path-dependent, but qV = ΔU and qp = ΔH make them appear like state functions only under those specific constraints.
• Free expansion of an ideal gas. w = 0 (because pext = 0) and q = 0 and ΔU = 0 — students often write w ≠ 0 because volume changes. No work because external pressure is zero, no heat because temperature does not change.
• ΔfH° of an element in its reference state is zero, not "unity" or "different for each element" — a frequent NCERT exercise trap (Ex. 5.3). But ΔfH° of an element in a non-reference state (e.g., O₃ from O₂, or C(diamond) instead of C(graphite)) is NOT zero.
• Spontaneity ≠ fast. A reaction can be spontaneous (ΔG < 0) yet extremely slow (H₂ + O₂ mixture at room T). Thermodynamics is silent on rate; kinetics handles speed.
• Entropy of surroundings. ΔSsurr = −ΔHsys/T (heat lost by system at temperature T is gained by surroundings). Negative ΔSsys can still give ΔStotal > 0 if ΔHsys is sufficiently negative.
• Bond enthalpy method gives ΔrH for gas-phase reactions only. If any reactant/product is in solid or liquid state, you must add appropriate phase-change enthalpies; otherwise the calculated ΔrH is wrong.
• Reversible work is the maximum the system can deliver; irreversible work is always smaller in magnitude. Students sometimes use the same w for both — wrong.
• ΔG° is a standard-state quantity at 1 bar (and the chosen T). ΔrG itself depends on actual concentrations: ΔrG = ΔrG° + RT ln Q; equilibrium reached when Q = K and ΔrG = 0, giving ΔrG° = −RT ln K.
• Heat capacity is extensive; specific heat and molar heat capacity are intensive. A common slip in MCQ definitions.