Physics · Thermal Physics and Properties of Matter

Thermodynamics formulas for JEE

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

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32 formulas1 concepts
01Laws of Thermodynamics
01

Laws of Thermodynamics

32 formulas

Adiabatic Process Equation (P-V)

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

Pressure-volume relationship during an adiabatic process.

applies whenReversible adiabatic process; Ideal gas.
thermodynamicsadiabaticideal_gas

Adiabatic Process Equation (P-T)

P1−γTγ=constantP^{1-\gamma}T^\gamma = \text{constant}

Pressure-temperature relationship during an adiabatic process.

applies whenReversible adiabatic process; Ideal gas.
thermodynamicsadiabaticideal_gasjee-advanced

Adiabatic Process Equation (T-V)

TVγ−1=constantTV^{\gamma-1} = \text{constant}

Temperature-volume relationship during an adiabatic process.

applies whenReversible adiabatic process; Ideal gas.
thermodynamicsadiabaticideal_gas

Work Done in Adiabatic Process

W=P1V1−P2V2γ−1=μR(T1−T2)γ−1W = \frac{P_1 V_1 - P_2 V_2}{\gamma - 1} = \frac{\mu R (T_1 - T_2)}{\gamma - 1}

Work calculated for an ideal gas expanding/compressing adiabatically.

applies whenReversible adiabatic process; Ideal gas.
thermodynamicsadiabaticwork

Carnot Engine Efficiency

η=1−T2T1=1−Q2Q1\eta = 1 - \frac{T_2}{T_1} = 1 - \frac{Q_2}{Q_1}

Maximum possible efficiency for a heat engine operating between two temperatures.

applies whenReversible heat engine.
thermodynamicscarnotefficiencyheat_engine

Carnot Cycle Universal Relation

Q1Q2=T1T2\frac{Q_1}{Q_2} = \frac{T_1}{T_2}

Ratio of heat exchanges equal to the ratio of absolute temperatures.

applies whenReversible Carnot cycle.
thermodynamicscarnottemperature_scale

Specific Heats in Terms of Degrees of Freedom

Cv=f2R,  Cp=(f2+1)R,  γ=1+2fC_v = \frac{f}{2}R, \; C_p = \left(\frac{f}{2} + 1\right)R, \; \gamma = 1 + \frac{2}{f}

Relating Cv, Cp, and gamma to the degrees of freedom (f) of a gas molecule.

applies whenIdeal gas with f degrees of freedom.
thermodynamicsktgdegrees_of_freedomjee-advanced

Dulong-Petit Law

C=3RC = 3R

Molar specific heat capacity of solids at ordinary temperatures.

applies whenSolid elements at ordinary room temperatures (breaks down at low temperatures).
thermodynamicssolidsspecific_heat

Entropy Change for Ideal Gas

ΔS=μCvln⁡(T2T1)+μRln⁡(V2V1)\Delta S = \mu C_v \ln\left(\frac{T_2}{T_1}\right) + \mu R \ln\left(\frac{V_2}{V_1}\right)

Formula for the change in entropy between two states of an ideal gas.

applies whenIdeal gas.
thermodynamicsentropyideal_gasjee-advanced

First Law of Thermodynamics

ΔQ=ΔU+ΔW\Delta Q = \Delta U + \Delta W

Conservation of energy for a thermodynamic system, relating heat, internal energy, and work.

applies whenApplicable to any thermodynamic process.
thermodynamicsfirst_lawenergy

First Law (Differential Form)

dQ=dU+dWdQ = dU + dW

Differential form of the First Law of Thermodynamics.

applies whenApplicable for infinitesimal quasi-static processes.
thermodynamicsfirst_lawdifferentialjee-advanced

Ratio of Specific Heats

γ=CpCv\gamma = \frac{C_p}{C_v}

Definition of the adiabatic exponent gamma.

thermodynamicsgammaspecific_heat

Heat Capacity

S=ΔQΔTS = \frac{\Delta Q}{\Delta T}

Amount of heat required to raise the temperature of a substance by one unit.

thermodynamicsheat_capacity

Ideal Gas Equation

PV=μRTPV = \mu RT

Equation of state for an ideal gas.

applies whenIdeal gas limit (low pressure, high temperature).
thermodynamicsideal_gasequation_of_state

Heat Exchange at Constant Pressure

ΔQ=μCpΔT\Delta Q = \mu C_p \Delta T

Heat absorbed or released during an isobaric process.

applies whenConstant pressure (Isobaric).
thermodynamicsisobaricheat

Work Done in Isobaric Process

W=P(V2−V1)=μR(T2−T1)W = P(V_2 - V_1) = \mu R(T_2 - T_1)

Work done by an ideal gas at constant pressure.

applies whenConstant pressure (Isobaric); Ideal Gas.
thermodynamicsisobaricwork

Heat Exchange at Constant Volume

ΔQ=ΔU=μCvΔT\Delta Q = \Delta U = \mu C_v \Delta T

Heat absorbed or released during an isochoric process.

applies whenConstant volume (Isochoric).
thermodynamicsisochoricheat

Isothermal Process Equation

PV=constantPV = \text{constant}

Pressure-volume relationship during an isothermal process (Boyle's Law).

applies whenConstant temperature (Isothermal); Ideal gas.
thermodynamicsisothermalideal_gas

Work Done in Isothermal Process

W=μRTln⁡(V2V1)W = \mu RT \ln\left(\frac{V_2}{V_1}\right)

Work calculated for an ideal gas expanding/compressing at constant temperature.

applies whenConstant temperature (Isothermal); Ideal gas.
thermodynamicsisothermalwork

Latent Heat Formula

ΔQ=mL\Delta Q = m L

Heat required to undergo a phase transition without changing temperature.

applies whenPhase transition at constant temperature.
thermodynamicslatent_heatphase_changejee-advanced

Mayer's Relation

Cp−Cv=RC_p - C_v = R

Relationship between molar heat capacity at constant pressure and constant volume.

applies whenIdeal gas.
thermodynamicsideal_gasspecific_heat

Gamma of a Gas Mixture

γmix=n1Cp1+n2Cp2n1Cv1+n2Cv2\gamma_{mix} = \frac{n_1 C_{p1} + n_2 C_{p2}}{n_1 C_{v1} + n_2 C_{v2}}

Ratio of specific heats for a non-reacting mixture of ideal gases.

applies whenNon-reacting ideal gas mixture.
thermodynamicsmixturegammajee-advanced

Molar Specific Heat Capacity

C=ΔQμΔTC = \frac{\Delta Q}{\mu \Delta T}

Heat required per mole to raise the temperature by one unit.

thermodynamicsmolar_heatmoles

Work Done During Phase Transition

W=P(Vg−Vl)W = P(V_g - V_l)

Expansion work done against atmospheric pressure during boiling/melting.

applies whenConstant pressure phase change.
thermodynamicsphase_changework

Polytropic Process Equation

PVn=constantPV^n = \text{constant}

General process equation governing ideal gases.

applies whenReversible polytropic process (n is constant); Ideal gas.
thermodynamicspolytropicideal_gasjee-advanced

Polytropic Molar Heat Capacity

C=Cv+R1−nC = C_v + \frac{R}{1-n}

Molar heat capacity of a gas undergoing a polytropic process.

applies whenReversible polytropic process; Ideal gas.
thermodynamicspolytropicmolar_heatjee-advanced

Work Done in Polytropic Process

W=P1V1−P2V2n−1=μR(T1−T2)n−1W = \frac{P_1 V_1 - P_2 V_2}{n - 1} = \frac{\mu R(T_1 - T_2)}{n - 1}

Work done by a gas during a polytropic process.

applies whenReversible polytropic process; Ideal gas.
thermodynamicspolytropicworkjee-advanced

Refrigerator Coefficient of Performance

β=Q2W=T2T1−T2\beta = \frac{Q_2}{W} = \frac{T_2}{T_1 - T_2}

Efficiency metric for a Carnot refrigerator or heat pump.

applies whenIdeal reversible refrigerator.
thermodynamicsrefrigeratorcopjee-advanced

Specific Heat Capacity

s=ΔQmΔTs = \frac{\Delta Q}{m \Delta T}

Heat required per unit mass to raise the temperature by one unit.

thermodynamicsspecific_heatmass

Rate of Heat Conduction

H=−KAdTdxH = -KA \frac{dT}{dx}

Fourier's law for the rate of heat conduction.

applies whenSteady state heat flow.
thermodynamicsheat_transferconduction

Volume Expansion Coefficient

αv=3α1\alpha_v = 3\alpha_1

Relation between the coefficient of volume expansion and linear expansion.

applies whenIsotropic solids.
thermodynamicsthermal_expansionsolids

Work Done by a Gas

W=∫V1V2P dVW = \int_{V_1}^{V_2} P \, dV

Integral formulation for work done during volume expansion/compression.

applies whenReversible (quasi-static) process.
thermodynamicsworkintegration
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