Chapter 12 – Thermodynamic Processes & Thermochemistry

Thermodynamics: macroscopic, operational science predicting feasibility, direction & quantitative details of physical/chemical processes.
Laws derived empirically; universal validity from black-holes to cells.
Independent of atomic theory (would survive its demise) but limited: cannot predict rates or precise property values; needs complementary kinetics/stat-mech.
Practical value: prevents wasting resources on impossible conditions; guides optimisation.

System: portion of universe chosen for study.
- Closed → no matter exchange ; Open → matter exchange ; Isolated → no matter/energy.
- Rigid vs non-rigid walls (mechanical); Adiabatic vs diathermal walls (thermal).
Surroundings: everything exchanging matter/energy with system.
Thermodynamic universe = system + surroundings (isolated overall).
Extensive vs Intensive:
- Extensive add on division (V, m, U).
- Intensive unchanged on division (T, P).
Thermodynamic state: macroscopic condition where properties fixed & time-independent.
- Defined by constraints; equilibrium when disturbances cease.
- For 1 mol ideal gas: state fixed by any 2 independent variables (e.g., P & T). $PV=nRT$ gives full surface (Fig 12.1).
Processes
- Change of state; physical or chemical.
- Reversible: passes through continuous sequence of equilibrium states; infinitesimally slow; path can be reversed by infinitesimal change.
- Irreversible: real; intermediate states non-equilibrium; cannot map on P-V-T surface.
- State functions (U, V, T, H …) depend only on initial & final states; Δ independent of path.

Work (w): $w=F\Delta x$ ; for P–V work under constant $P{ext}$ , $w=-P{ext}\,\Delta V$ (Eq 12.1). Sign convention: work done on system positive.
Heat (q): energy transfer due to T difference. Measured via calorimetry.
- Ice calorimeter (volume contraction as ice melts).
- Relation: $q = M c_s \Delta T$ (Eq 12.2).
- Historical 1 cal = 4.184 J.
Internal Energy (U): total microscopic E (molecular KE + PE + chemical). State function.
First Law: $\Delta U = q + w \quad (\text{system})$ (Eq 12.3).
- Energy conserved: $\Delta U_{univ}=0$ (Eq 12.4).
Process examples:
- Expansion of gas against 1 atm (Example 12.1) → system does work, U decreases.
- Joule paddle experiment illustrates equivalence of work & heat.

Heat capacity (C): heat required for 1 K rise. $q=C\,\Delta T$ .
Molar/specific capacities; two varieties:
- $CV$ (constant V) & $CP$ (constant P); $CP>CV$ for gases.
Coffee-cup calorimeter example (Fe in water) illustrates energy balance.
Bomb calorimetry: constant V combustion → $\Delta U=q_V$ .
Enthalpy $H=U+PV$ (Eq 12.7a).
- At constant P with only P–V work: $\Delta H = q_P$ (Eq 12.7b).
- Links: $\Delta H = \Delta U + P\Delta V$ .

For ideal gases $U, H$ depend only on T.
Heat capacities (kinetic-theory):
- Monatomic: $cV = \frac{3}{2}R$ (Eq 12.8); $cP = \frac{5}{2}R$ .
- General: $cP = cV + R$ (Eq 12.9).
- $\Delta U = n cV \Delta T$ (Eq 12.10); $\Delta H = n cP \Delta T$ (Eq 12.11).
Path-dependence illustrated (Fig 12.10): two routes ACB & ADB yield same $\Delta U$ (1520 J) but different q, w values.

Degrees of freedom (f) & equipartition: each quadratic term contributes $\frac{1}{2}RT$ per mol to U.
- Translational: 3.
- Rotational: 2 (linear) or 3 (non-linear).
- Vibrational: each mode contributes both KE & PE → $RT$ (per mode).
Tables 12.2-12.3 compare predicted vs experimental $c_P$ .
- Diatomics reach translational + rotational ((7/2)R) at room T; vibrational modes activate at high T (Fig 12.12).
Solids: Dulong–Petit $c_V≈3R$ at high T; quantum models (Einstein, Debye) explain low-T drop (Fig 12.13).

Reaction enthalpy (ΔH): heat at const P for stoichiometric equation.
- Exothermic ΔH<0 (e.g., thermite; Fig 12.14).
- Endothermic ΔH>0 (Ba(OH)₂·8H₂O + NH₄NO₃; Fig 12.15).
Hess’s Law: reaction ΔH found by algebraic addition of steps; because H is state function.
Phase enthalpies: fusion ΔHfus, vaporization ΔHvap (Table 12.4).
Standard state (°)
- 1 atm, specified T (usually 298.15 K), pure phase or 1 m solution.
- Elements in most stable form assigned $H^{°}=0$ (except P white).
Standard enthalpy of formation $\Delta H_f^{°}$ : enthalpy to form 1 mol compound from elements in std states.
- Reaction enthalpy: $\Delta H^{°} = \sum ni\,\Delta H{f,i}^{°}(\text{products}) - \sum nj\,\Delta H{f,j}^{°}(\text{reactants})$ (Eq 12.12).
Bond enthalpies (Table 12.5): average gas-phase values enable estimation of (\Delta H_f^{°}) when tabulated data absent (Example 12.9).

Isothermal (T const)
- $\Delta U = \Delta H =0$ .
- $w = -nRT\ln\frac{V2}{V1} = nRT\ln\frac{P1}{P2}$ .
- $q = -w$ to keep T constant (Example 12.10).
Adiabatic (q=0)
- $nc_V dT = -P\,dV$ .
- Relations (γ=cP/cV): $T V^{\gamma-1}=\text{const};\; P V^{\gamma}=\text{const}$ (Eqs 12.17–12.18).
- Work equals change in U: $w = n cV (T2-T1)$ ; enthalpy via $n cP\Delta T$ .
- Expansion cools gas (Example 12.11); adiabatic curve steeper than isotherm (Fig 12.20).

Probability of molecule in state n: $P(n)=C\,e^{-\varepsilonn/kB T}$ (Eq 12.19).
For harmonic oscillator (vibration): $\varepsilon_n = (n+\frac12)h\nu$ .
- Relative population: $\frac{P(n)}{P(0)} = e^{-n h \nu /k_B T}$ (Eq 12.22).
CO example: $h\nu=4.52\times10^{-20}\,\text{J}$ ; at 300 K only 3×10⁻⁵ of molecules in v=1.
Br₂ example (Example 12.12): lower force constant → much smaller hν, so significant vibrational population even at 300 K (Fig 12.21).