CHEMCA
EXAM MASTER FORMULA SHEET
Thermodynamics & Thermochemistry
Critical Concepts for JEE Main, Advanced & NEET
1. First Law of Thermodynamics
The Governing Equation:
\[ \Delta U = q + w \]
Sign Convention (IUPAC): Work done ON the system is (+), heat added TO the system is (+).
Internal Energy (\(U\)):
\[ \Delta U = n C_v \Delta T \]
(Always for Ideal Gas)
Enthalpy (\(H\)):
\[ \Delta H = \Delta U + \Delta(PV) = \Delta U + \Delta n_g RT \]
2. Work Formulas for Ideal Gases
| Process | Irreversible Work (\(w\)) | Reversible Work (\(w\)) |
|---|---|---|
| Isothermal | \( -P_{ext}(V_2 - V_1) \) | \( -2.303 nRT \log(V_2/V_1) \) |
| Isobaric | \( -P \Delta V \) | \( -P \Delta V \) |
| Isochoric | 0 | 0 |
| Adiabatic | \( nC_v(T_2 - T_1) \) | \( \frac{P_2V_2 - P_1V_1}{\gamma - 1} \) |
3. Heat Capacity & Poisson's Ratio
Mayer's Formula:
\( C_p - C_v = R \)
Poisson's Ratio (\(\gamma\)):
\( \gamma = \frac{C_p}{C_v} = 1 + \frac{2}{f} \)
Degrees of Freedom (\(f\)):
Monoatomic: \(f=3, \gamma=1.66\)
Diatomic: \(f=5, \gamma=1.40\)
Polyatomic: \(f=6, \gamma=1.33\)
4. Thermochemistry
Standard Enthalpy of Reaction (\(\Delta_r H^\circ\)):
\[ \Delta_r H^\circ = \sum \Delta_f H^\circ_{products} - \sum \Delta_f H^\circ_{reactants} \]
Bond Enthalpy Method:
\[ \Delta H = \sum B.E._{reactants} - \sum B.E._{products} \]
Resonance Energy:
\[ \Delta H_{obs} - \Delta H_{calc} \]
5. Entropy & Gibbs Free Energy
Entropy (\(S\)):
\[ \Delta S = \frac{q_{rev}}{T} \]
Isothermal: \( \Delta S = nR \ln(V_2/V_1) \)
Gibbs Free Energy (\(G\)):
\[ \Delta G = \Delta H - T \Delta S \]
Criteria for Spontaneity:
\(\Delta G < 0\)
Spontaneous
Spontaneous
\(\Delta G = 0\)
Equilibrium
Equilibrium
\(\Delta G > 0\)
Non-Spontaneous
Non-Spontaneous
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