Chemistry · Physical Chemistry

Chemical Thermodynamics formulas for JEE

Every Chemical Thermodynamics formula you need for JEE, grouped by concept.

FormulasRevision notes
34 formulas4 concepts
01Thermodynamic Basics and Terminology02First Law of Thermodynamics03Second Law and Spontaneity04Hess's Law and Enthalpy Calculations
01

Thermodynamic Basics and Terminology

4 formulas

Heat Capacity

q=CΔTq = C \Delta T

Heat transfer related to total heat capacity.

applies whenNo phase change.
thermodynamicsheat capacity

Molar Heat Capacity

Cm=CnC_m = \frac{C}{n}

Molar heat capacity definition.

thermodynamicsheat capacitymolar

Mayer's Relation

Cp−Cv=RC_p - C_v = R

Relationship between molar heat capacities at constant pressure and volume.

applies whenIdeal gas.
thermodynamicsheat capacityideal gas

Poisson's Equation (Adiabatic)

PVγ=constantPV^\gamma = \text{constant}

Pressure-volume relation for reversible adiabatic processes.

applies whenReversible adiabatic process, ideal gas.
thermodynamicsadiabaticjee-advanced
02

First Law of Thermodynamics

15 formulas

Heat Capacity

q=CΔTq = C \Delta T

Heat transfer related to total heat capacity.

applies whenNo phase change.
thermodynamicsheat capacity

Molar Heat Capacity

Cm=CnC_m = \frac{C}{n}

Molar heat capacity definition.

thermodynamicsheat capacitymolar

Bomb Calorimetry Heat Transfer

qv=CvΔT=ΔUq_v = C_v \Delta T = \Delta U

Heat absorbed/evolved at constant volume.

applies whenConstant volume, no non-expansion work.
thermodynamicscalorimetrybomb calorimeter

Constant Pressure Calorimetry

qp=CpΔT=ΔHq_p = C_p \Delta T = \Delta H

Heat absorbed/evolved at constant pressure.

applies whenConstant pressure.
thermodynamicscalorimetry

Enthalpy Change (Ideal Gas Reactions)

ΔH=ΔU+ΔngRT\Delta H = \Delta U + \Delta n_g RT

Relates enthalpy and internal energy changes for reactions involving gases.

applies whenIdeal gas behaviour, constant temperature and pressure.
thermodynamicsenthalpyideal gas

Enthalpy Change (Constant Pressure)

ΔH=ΔU+pΔV\Delta H = \Delta U + p\Delta V

Change in enthalpy at constant pressure.

applies whenConstant pressure.
thermodynamicsenthalpy

Enthalpy Definition

H=U+pVH = U + pV

Definition of enthalpy as a state function.

applies whenConstant pressure conditions.
thermodynamicsenthalpydefinition

First Law of Thermodynamics

ΔU=q+w\Delta U = q + w

Mathematical statement of the first law of thermodynamics (IUPAC sign convention).

applies whenClosed system.
thermodynamicsfirst lawenergy

Mayer's Relation

Cp−Cv=RC_p - C_v = R

Relationship between molar heat capacities at constant pressure and volume.

applies whenIdeal gas.
thermodynamicsheat capacityideal gas

Specific Heat Capacity

q=mcΔTq = m c \Delta T

Heat transfer related to mass and specific heat.

applies whenNo phase change.
thermodynamicsheat capacityspecific heat

Irreversible PV Work

w=−pexΔV=−pex(Vf−Vi)w = -p_{ex} \Delta V = -p_{ex}(V_f - V_i)

Work done against a constant external pressure.

applies whenIrreversible process against constant external pressure.
thermodynamicsworkirreversible

Irreversible PV Work (Multi-step)

w=−∑pΔVw = - \sum p \Delta V

Total work done when pressure changes in finite steps.

applies whenIrreversible multi-step process.
thermodynamicsworkirreversible

Reversible PV Work

wrev=−∫ViVfpindVw_{rev} = - \int_{V_i}^{V_f} p_{in} dV

Work done during an infinitely slow, reversible volume change.

applies whenReversible process.
thermodynamicsworkreversible

Reversible Adiabatic Work

w=nR(T2−T1)γ−1w = \frac{nR(T_2 - T_1)}{\gamma - 1}

Work done during a reversible adiabatic expansion/compression of an ideal gas.

applies whenReversible adiabatic process, ideal gas.
thermodynamicsworkadiabaticjee-advanced

Reversible Isothermal Work

wrev=−2.303nRTlog⁡(VfVi)w_{rev} = -2.303 nRT \log \left(\frac{V_f}{V_i}\right)

Work done in a reversible isothermal expansion/compression of an ideal gas.

applies whenIsothermal reversible process for an ideal gas.
thermodynamicsworkisothermalideal gas
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03

Second Law and Spontaneity

10 formulas

Gibbs Free Energy Definition

G=H−TSG = H - TS

Definition of Gibbs free energy.

thermodynamicsgibbs

Standard Gibbs Energy and Equilibrium

ΔrG⊖=−RTln⁡K=−2.303RTlog⁡K\Delta_r G^\ominus = -RT \ln K = -2.303 RT \log K

Relationship between standard Gibbs energy and the equilibrium constant.

applies whenEquilibrium condition.
thermodynamicsgibbsequilibrium

Carnot Engine Efficiency

η=1−TcTh\eta = 1 - \frac{T_c}{T_h}

Maximum theoretical efficiency of a heat engine.

applies whenReversible cyclic process.
thermodynamicsefficiencycarnotjee-advanced

Clausius-Clapeyron Equation

ln⁡(P2P1)=ΔvapHR(1T1−1T2)\ln\left(\frac{P_2}{P_1}\right) = \frac{\Delta_{vap} H}{R} \left(\frac{1}{T_1} - \frac{1}{T_2}\right)

Relationship between vapor pressure and temperature during phase transition.

applies whenLiquid-vapor phase equilibrium.
thermodynamicsphase equilibriumjee-advanced

Entropy Definition

ΔS=qrevT\Delta S = \frac{q_{rev}}{T}

Change in entropy for a reversible process.

applies whenReversible process.
thermodynamicsentropy

Entropy Change of an Ideal Gas (T, V)

ΔS=nCvln⁡(T2T1)+nRln⁡(V2V1)\Delta S = nC_v \ln\left(\frac{T_2}{T_1}\right) + nR \ln\left(\frac{V_2}{V_1}\right)

Entropy change in terms of temperature and volume.

applies whenIdeal gas.
thermodynamicsentropyideal gasjee-advanced

Entropy Change of an Ideal Gas (T, P)

ΔS=nCpln⁡(T2T1)−nRln⁡(P2P1)\Delta S = nC_p \ln\left(\frac{T_2}{T_1}\right) - nR \ln\left(\frac{P_2}{P_1}\right)

Entropy change in terms of temperature and pressure.

applies whenIdeal gas.
thermodynamicsentropyideal gasjee-advanced

Total Entropy Change

ΔStotal=ΔSsys+ΔSsurr>0\Delta S_{total} = \Delta S_{sys} + \Delta S_{surr} > 0

Second Law of Thermodynamics criterion for spontaneity.

applies whenSpontaneous process.
thermodynamicsentropyspontaneity

Gibbs Free Energy Change

ΔG=ΔH−TΔS\Delta G = \Delta H - T\Delta S

Change in Gibbs energy at constant temperature.

applies whenConstant temperature.
thermodynamicsgibbs

Gibbs Energy and Non-Expansion Work

ΔGsys=wnon−expansion\Delta G_{sys} = w_{non-expansion}

Standard Gibbs energy corresponds to the maximum non-expansion (useful) work.

applies whenConstant temperature and pressure.
thermodynamicsgibbsworkjee-advanced
04

Hess's Law and Enthalpy Calculations

5 formulas

Reaction Enthalpy from Bond Enthalpies

ΔrH⊖=∑ΔbondH⊖(reactants)−∑ΔbondH⊖(products)\Delta_r H^\ominus = \sum \Delta_{bond} H^\ominus(\text{reactants}) - \sum \Delta_{bond} H^\ominus(\text{products})

Approximation of reaction enthalpy using mean bond enthalpies.

applies whenGaseous phase reactants and products.
thermodynamicsenthalpybond enthalpy

Standard Reaction Enthalpy

ΔrH⊖=∑aiΔfH⊖(products)−∑biΔfH⊖(reactants)\Delta_r H^\ominus = \sum a_i \Delta_f H^\ominus(\text{products}) - \sum b_i \Delta_f H^\ominus(\text{reactants})

Reaction enthalpy calculated from standard enthalpies of formation.

applies whenStandard states.
thermodynamicsenthalpyreaction

Hess's Law

ΔrH=ΔrH1+ΔrH2+…\Delta_r H = \Delta_r H_1 + \Delta_r H_2 + \dots

Enthalpy change of an overall reaction is the sum of intermediate steps.

applies whenConstant temperature and pressure.
thermodynamicsenthalpyhess law

Kirchhoff's Equation

ΔrH⊖(T)=ΔrH⊖(0)+∫0TΔrCp⊖dT\Delta_r H^\ominus(T) = \Delta_r H^\ominus(0) + \int_0^T \Delta_r C_p^\ominus dT

Temperature dependence of the enthalpy of reaction.

applies whenConstant pressure.
thermodynamicsenthalpytemperature dependence

Enthalpy of Solution

ΔsolH⊖=ΔlatticeH⊖+ΔhydH⊖\Delta_{sol} H^\ominus = \Delta_{lattice} H^\ominus + \Delta_{hyd} H^\ominus

Enthalpy of solution derived via Born-Haber cycle.

applies whenStandard states.
thermodynamicsenthalpysolution
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