Thermodynamics

🟢 Lite — Quick Review (1h–1d)

Rapid summary for last-minute revision before your exam.

Thermodynamics — Key Facts for CUET First law: $\Delta U = q + w$; $w = -P\Delta V$ (expansion work, sign convention: work done BY system is negative) Enthalpy: $H = U + PV$; for constant pressure: $\Delta H = q_p = \Delta U + P\Delta V$ Hess’s law: $\Delta H_{\text{reaction}} = \sum \Delta H_f°(\text{products}) - \sum \Delta H_f°(\text{reactants})$ Standard enthalpy of formation: $\Delta H_f°$ of elements in standard state = 0 Bond enthalpy: energy to break 1 mole of bond; reaction enthalpy $\approx \sum \Delta H_{\text{bonds broken}} - \sum \Delta H_{\text{bonds formed}}$ ⚡ Exam tip: For a cyclic process, $\Delta U = 0$ and $\Delta H = 0$; for isothermal expansion of ideal gas, $\Delta U = 0$, so $q = -w$

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🟡 Standard — Regular Study (2d–2mo)

For students who want genuine understanding of energy changes in chemical reactions.

Thermodynamics — CUET Chemistry Study Guide

Thermodynamics studies energy changes (heat and work) during physical and chemical processes. The three laws of thermodynamics provide a framework for predicting whether a process is spontaneous.

First Law of Thermodynamics (Energy Conservation): Energy can neither be created nor destroyed. $\Delta U = q + w$, where $U$ is internal energy, $q$ is heat added to system, and $w$ is work done on system. Internal energy is a state function (path-independent). For ideal gases, $\Delta U = nC_V\Delta T$ (depends only on temperature).

Work in Chemical Reactions: The most common work is pressure-volume work. For expansion against constant external pressure $P$: $w = -P\Delta V$. For reversible (infinitely slow) expansion: $w_{\text{rev}} = -\int P_{\text{ext}}dV = -nRT\ln\frac{V_f}{V_i}$.

Enthalpy ($H$): $H = U + PV$. At constant pressure, the heat transferred equals the change in enthalpy: $q_p = \Delta H$. Like $U$, $H$ is a state function. For ideal gases, $\Delta H = nC_P\Delta T$. The difference $C_P - C_V = R$ for ideal gases.

Hess’s Law: The enthalpy change of a reaction is independent of the path taken — it depends only on the initial and final states. This allows us to calculate $\Delta H$ for difficult-to-measure reactions using known enthalpies. Example: C(s) + ½O₂(g) → CO(g) cannot be measured directly (produces mixture), but $\Delta H$ can be found from C(s) + O₂(g) → CO₂(g) and CO(g) + ½O₂(g) → CO₂(g).

Enthalpy of Reaction: $\Delta H°_{\text{rxn}} = \sum n_p \Delta H_f°(\text{products}) - \sum n_r \Delta H_f°(\text{reactants})$. Standard enthalpy of formation $\Delta H_f°$ is the enthalpy change when 1 mole of compound forms from its elements in their standard states. $\Delta H_f°$ of elements in their standard states = 0.

Born-Haber Cycle: Used to calculate lattice energy of ionic compounds. For NaCl: $\Delta H_f° = \Delta H_{\text{atomisation}}(Na) + \frac{1}{2}\Delta H_{\text{bond dissociation}}(Cl_2) + \Delta H_{\text{ionisation}}(Na) + \Delta H_{\text{electron affinity}}(Cl) + \Delta H_{\text{lattice}}$. Since lattice energy cannot be measured directly, it is extracted from the cycle.

Example: Calculate $\Delta H°$ for combustion of methane: CH₄(g) + 2O₂(g) → CO₂(g) + 2H₂O(l). $\Delta H° = [\Delta H_f°(CO₂) + 2\Delta H_f°(H₂O)] - [\Delta H_f°(CH₄) + 2\Delta H_f°(O₂)]$ $= [-393.5 + 2(-285.8)] - [-74.8 + 0] = -965.1 + 74.8 = -890.3$ kJ/mol.

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🔴 Extended — Deep Study (3mo+)

Comprehensive coverage for students on a longer study timeline.

Thermodynamics — Complete CUET Chemistry Notes

Second Law of Thermodynamics: Heat cannot be completely converted to work in a cyclic process. The universe tends toward maximum disorder (entropy). Spontaneous processes increase total entropy of the universe. $\Delta S_{\text{universe}} = \Delta S_{\text{system}} + \Delta S_{\text{surroundings}} > 0$ for spontaneous processes.

Entropy ($S$): A state function measuring disorder. For a reversible process: $\Delta S = \frac{q_{\text{rev}}}{T}$. Statistical interpretation: $S = k_B \ln W$, where $W$ is number of microstates. More microstates = higher entropy. Gases > liquids > solids (more disorder). Entropy increases with temperature and volume.

Third Law of Thermodynamics: At absolute zero (0 K), the entropy of a perfect crystal is zero ($S = 0$ at 0 K). This provides a reference point for absolute entropies. Standard molar entropy $S°$ of substances can be found from heat capacity measurements: $S° = \int_0^{298}\frac{C_P}{T}dT$.

Gibbs Free Energy ($G$): $G = H - TS$. At constant temperature and pressure: $\Delta G = \Delta H - T\Delta S$. Spontaneous if $\Delta G < 0$. $\Delta G = 0$ at equilibrium. $\Delta G° = -RT\ln K$ links thermodynamics to equilibrium constant.

Conditions	$\Delta H$	$\Delta S$	$\Delta G$	Spontaneous?
Both favorable	−	+	−	Always
Low temperature	−	−	− (if $T < \frac{\Delta H}{\Delta S}$)	Low T only
High temperature	+	+	− (if $T > \frac{\Delta H}{\Delta S}$)	High T only
Both unfavorable	+	−	+	Never

Thermochemistry in Real Processes:

• Ionisation enthalpy: energy needed to remove electron from gaseous atom
• Electron affinity: energy released when electron added to gaseous atom (usually exothermic, except for O, S)
• Lattice enthalpy: energy released when gaseous ions form solid lattice (always exothermic)

Kirchhoff’s Law: $\Delta H$ at temperature $T_2$: $\Delta H_{T_2} = \Delta H_{T_1} + \int_{T_1}^{T_2}\Delta C_P dT$. Similarly for $\Delta S$ and $\Delta G$.

CUET Exam Patterns (2022–2024):

• Hess’s law and enthalpy calculations are most frequent (1–2 marks)
• First law problems ($\Delta U = q + w$) appear every year
• Relationship $\Delta G = \Delta H - T\Delta S$ is commonly tested
• Born-Haber cycle and lattice energy occasionally appear
• Common mistakes: forgetting sign conventions for $q$ and $w$; confusing $\Delta H$ and $\Delta U$; using wrong units (kJ vs J)

⚡ Key insight: In thermodynamics, always be careful about the sign convention. Heat absorbed by system is positive ($+q$), heat released is negative ($-q$). Work done by system on surroundings is negative ($-w$), work done on system is positive ($+w$). The system loses energy when it does work on surroundings or releases heat.

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