Chemca Formula Sheet - Thermodynamics

CHEMCA

EXAM MASTER FORMULA SHEET

Thermodynamics & Thermochemistry

Ultimate Revision for JEE Main, Advanced & NEET

1. System Properties & First Law

Extensive vs Intensive

• Extensive (Depends on mass): Volume (V), Mass (m), Internal Energy (U), Enthalpy (H), Entropy (S), Gibbs Energy (G), Heat Capacity (C).
• Intensive (Independent of mass): Temperature (T), Pressure (P), Density (d), Specific Heat (s), Molar Heat Capacity ($C_m$), EMF of cell ($E_{cell}$), pH, Refractive Index.

State vs Path Functions

• State Functions: Depend only on initial and final states. E.g., $\Delta U, \Delta H, \Delta S, \Delta G, \Delta P, \Delta V, \Delta T$. (Note: $\oint dX = 0$)
• Path Functions: Depend on the path taken. E.g., Heat ($q$), Work ($w$).

First Law of Thermodynamics (FLOT):

\[ \Delta U = q + w \]

IUPAC Sign Convention:
$w = (+)$ Work done ON the system (Compression)
$w = (-)$ Work done BY the system (Expansion)

$q = (+)$ Heat ADDED to system (Endothermic)
$q = (-)$ Heat LOST by system (Exothermic)

Internal Energy ($\Delta U$) & Enthalpy ($\Delta H$):

\[ \Delta U = n C_v \Delta T = q_v \] \[ \Delta H = n C_p \Delta T = q_p \]

\[ \Delta H = \Delta U + \Delta n_g RT \]

$\Delta n_g = (\text{moles of gaseous products}) - (\text{moles of gaseous reactants})$

Heat Capacity Relations:

\[ C_p - C_v = R \text{ (Mayer's Formula)} \] \[ \gamma = \frac{C_p}{C_v} = 1 + \frac{2}{f} \]

Mono: $f=3$

Dia: $f=5$

Poly: $f=6$

2. Work Formulas for Ideal Gases

Process	Irreversible Work ($w_{irr}$)	Reversible Work ($w_{rev}$)
Isobaric ($P=$ const)	\( -P_{ext}(V_2 - V_1) \)	\( -P(V_2 - V_1) = -nR(T_2 - T_1) \)
Isochoric ($V=$ const)	0	0
Isothermal ($T=$ const)	\( -P_{ext}(V_2 - V_1) \)	\( -2.303 nRT \log\left(\frac{V_2}{V_1}\right) = -2.303 nRT \log\left(\frac{P_1}{P_2}\right) \)
Adiabatic ($q=0$)	\( -P_{ext}(V_2 - V_1) = nC_v(T_2 - T_1) \)	\( \frac{nR(T_2 - T_1)}{\gamma - 1} = \frac{P_2V_2 - P_1V_1}{\gamma - 1} \)

Free Expansion (Expansion in Vacuum): Since external pressure $P_{ext} = 0$, work done **$w = 0$** (always, whether reversible/irreversible, isothermal/adiabatic).

Isothermal Free Expansion:
$w=0, \Delta U=0, q=0$

3. Entropy ($S$) & Second Law of Thermodynamics

Second Law (Spontaneity):

For any spontaneous process, the total entropy of the universe must increase.

\[ \Delta S_{universe} = \Delta S_{system} + \Delta S_{surr} \ge 0 \]

Basic Entropy Change:

\[ \Delta S = \frac{q_{rev}}{T} \]

At phase change: $\Delta S_{fus} = \frac{\Delta H_{fus}}{T_m}$ , $\Delta S_{vap} = \frac{\Delta H_{vap}}{T_b}$

Entropy Change of an Ideal Gas:

\[ \Delta S = nC_v \ln\left(\frac{T_2}{T_1}\right) + nR \ln\left(\frac{V_2}{V_1}\right) \]

\[ \Delta S = nC_p \ln\left(\frac{T_2}{T_1}\right) + nR \ln\left(\frac{P_1}{P_2}\right) \]

For Isothermal processes ($T_1=T_2$), the first term becomes zero. For Isochoric ($V_1=V_2$), the second term is zero.

4. Gibbs Free Energy ($G$) & Spontaneity

Gibbs-Helmholtz Equation:

\[ \Delta G = \Delta H - T \Delta S \]

Maximum non-expansion work obtainable from a system: $W_{non-exp, max} = -\Delta G$

Relation with Equilibrium Constant ($K_{eq}$):

\[ \Delta G = \Delta G^\circ + RT \ln Q \]

At Equilibrium ($\Delta G = 0, Q = K_{eq}$): \[ \Delta G^\circ = -2.303 RT \log K_{eq} \]

Spontaneity Matrix (Effect of Temp):

$\Delta H$	$\Delta S$	Spontaneity ($\Delta G = \Delta H - T\Delta S$)
$-$ (Exothermic)	$+$ (More random)	Spontaneous at ALL Temperatures
$+$ (Endothermic)	$-$ (Less random)	Non-spontaneous at ALL Temperatures
$-$ (Exothermic)	$-$ (Less random)	Spontaneous at Low Temperatures
$+$ (Endothermic)	$+$ (More random)	Spontaneous at High Temperatures

5. Thermochemistry

Hess's Law

Total enthalpy change for a reaction is the same whether it occurs in one step or multiple steps.

\[ \Delta_r H^\circ = \sum \Delta_f H^\circ_{\text{products}} - \sum \Delta_f H^\circ_{\text{reactants}} \]

Bond Enthalpy Method

Energy required to break one mole of bonds. Note: Reactants minus Products!

\[ \Delta_r H = \sum B.E._{\text{reactants}} - \sum B.E._{\text{products}} \]

Enthalpy of Neutralization:

Heat released when 1 gram equivalent of acid reacts with 1 gram equivalent of base.

For Strong Acid + Strong Base:
$\Delta_{neut} H \approx -57.1 \text{ kJ/mol} \text{ or } -13.7 \text{ kcal/mol}$

If weak acid/base is used, magnitude is less than 57.1 due to energy consumed in ionization.

Kirchhoff's Equation:

Variation of enthalpy of reaction with temperature.

\[ \Delta H_2 - \Delta H_1 = \Delta C_p (T_2 - T_1) \] \[ \Delta U_2 - \Delta U_1 = \Delta C_v (T_2 - T_1) \]

© 2026 CHEMCA Academy. All Rights Reserved.

Quiz Revision Notes Downloads Class Notes Video Lectures

🎯 Complete Chemistry Revision Toolkit

Score higher by combining Formula Sheets, Flashcards and the Mistake Bank. These three resources help you revise faster, remember longer and avoid common exam mistakes for JEE Main, JEE Advanced, NEET and CBSE Board.

📄 Formula Sheets

Quick chapter-wise formulas, equations, constants and revision charts for last-minute preparation.

🧠 Chemistry Flashcards

Revise using active recall with interactive flashcards covering important concepts, reactions and exceptions.

❌ Mistake Bank

Identify common mistakes, eliminate weak areas and improve your accuracy in competitive examinations.

💡 Best Revision Strategy: Start with Formula Sheets for quick revision, reinforce concepts using Flashcards, and finish with the Mistake Bank to avoid repeating errors in the examination.