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Thermodynamics revision notes

Every idea in the Thermodynamics chapter for JEE Main, with the usual mistakes and the fast methods. Topic 1 is open to everyone; sign in free to read all 31 and download the PDF.

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How we count: 7× asked means 7 past JEE Main questions in the PrepWiser bank needed that concept, and "last" is the latest year one appeared. ★ marks ideas asked 8 or more times.

Basics and the first law

Zeroth law and temperature
1× asked, last 2026
A↔C,  B↔C  ⇒  A↔BA \leftrightarrow C,\ \ B \leftrightarrow C \;\Rightarrow\; A \leftrightarrow B
↔\leftrightarrow = in thermal equilibrium. Bodies in equilibrium share one temperature; this law defines temperature.
Intensive and extensive variables
2× asked, last 2026
  • Not extensive for extensive ÷ mass or volume. That ratio (density, specific heat) is intensive. Extensive: mm, VV, UU, SS. Intensive: PP, TT, ρ\rho. Intensive × extensive is extensive.
Heat, work and internal energy
4× asked, last 2023
UU is a state function: ΔU\Delta U depends only on the end states. QQ and WW are path functions.
  • Not 'heat in means temperature rises'. In an isothermal expansion all the heat becomes work; during melting or boiling TT stays fixed. W>0W>0 means VV grew when VV changes one way; a cycle can give net W>0W>0 with ΔV=0\Delta V=0.
Ideal gas equation
PV=nRT,P1V1T1=P2V2T2PV = nRT,\qquad \frac{P_1V_1}{T_1}=\frac{P_2V_2}{T_2}
Fixed amount of ideal gas, any two states; TT in kelvin. A bubble at depth hh is at P0+ρghP_0+\rho gh.
  • Quick method. Connected vessels or mixed gases: total moles are conserved, so ∑PV/T\sum PV/T before = ∑PV/T\sum PV/T after, with one common pressure. A second condition (total mass) splits moles between gases.
  • Quick method. Mixing ideal gases in an insulated box conserves UU: Tf=∑niCV,iTi/∑niCV,iT_f=\sum n_iC_{V,i}T_i/\sum n_iC_{V,i}. For gases of the same type it is the mole-weighted mean of the temperatures.
First law of thermodynamics
13× asked, last 2026
ΔQ=ΔU+W,dQdt=dUdt+dWdt\Delta Q = \Delta U + W,\qquad \frac{dQ}{dt}=\frac{dU}{dt}+\frac{dW}{dt}
Q>0Q>0 heat into the gas, W>0W>0 work by the gas. If WW is work done on the gas: ΔQ=ΔU−W\Delta Q=\Delta U-W.
  • Phase change at constant PP: Q=mLQ=mL, W=PΔVW=P\Delta V, so ΔU=mL−PΔV\Delta U=mL-P\Delta V. For liquids and solids WW is tiny (ΔV\Delta V from V=m/ρV=m/\rho) but not zero.
  • Quick method. Gas pushing a free piston against the air: W=P0AxW=P_0Ax, so x=(Q−ΔU)/P0Ax=(Q-\Delta U)/P_0A. Convert cm² to m² first. A weight or spring on the piston takes its own share of the energy.
Internal energy of an ideal gas
9× asked, last 2026
ΔU=nCVΔT=nR ΔTγ−1=P2V2−P1V1γ−1\Delta U = nC_V\Delta T = \frac{nR\,\Delta T}{\gamma-1} = \frac{P_2V_2-P_1V_1}{\gamma-1}
Any process, not only isochoric: UU of an ideal gas depends on TT alone. Cycle or same isotherm: ΔU=0\Delta U=0.
  • Not nCPΔTnC_P\Delta T for ΔU\Delta U. Even at constant pressure ΔU=nCVΔT\Delta U=nC_V\Delta T; CPC_P gives the heat. Given CPC_P, take CV=CP−RC_V=C_P-R first, with R≈2R\approx2 cal/mol K in calorie problems.
Specific heats of an ideal gas
9× asked, last 2026
CV=f2R,CP=CV+R,γ=CPCV=1+2fC_V=\frac{f}{2}R,\qquad C_P=C_V+R,\qquad \gamma=\frac{C_P}{C_V}=1+\frac{2}{f}
ff = degrees of freedom (see Kinetic Theory). Monatomic 3, rigid diatomic 5, rigid nonlinear polyatomic 6.
  • For rigid molecules γ\gamma identifies the gas: 5/35/3 monatomic, 7/57/5 diatomic or linear (e.g. CO₂), 4/34/3 nonlinear polyatomic. Vibration adds to ff and lowers γ\gamma: a vibrating diatomic has 9/79/7.
  • Ideal gas: CP−CV=RC_P-C_V=R. For another equation of state whose UU still depends on TT only (e.g. PV2=RTPV^2=RT), use CP−CV=P(∂V/∂T)PC_P-C_V=P(\partial V/\partial T)_P.

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Practise Thermodynamics

24 more concepts in 5 topics

Work and P–V diagrams; Thermodynamic processes; Heat engines, refrigerators and Carnot; and Second law, reversibility and entropy, plus ideas from calorimetry, expansion, kinetic theory. Read the first part free. Sign in free with Google to read the rest and download the PDF.

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Work and P–V diagrams

  • Work done by a gas8×
  • Cyclic process12×
  • Processes on P–T and V–T graphs6×
  • Temperature along a path3×

Thermodynamic processes

  • Isochoric process7×
  • Isobaric process14×
  • Isothermal process11×
  • Adiabatic process7×
  • Adiabatic relations19×
  • Adiabatic work14×
  • Slopes on a P–V graph4×
  • Comparing work in different processes2×
  • Polytropic process5×
  • Molar heat capacity of a process6×
  • Volume expansion coefficient of a gas1×
  • Free expansion2×
  • Also remember1

Heat engines, refrigerators and Carnot

  • Heat engine5×
  • Carnot engine20×
  • Carnot cycle and Carnot's theorem5×
  • Engines in series4×
  • Refrigerator and heat pump3×

Second law, reversibility and entropy

  • Second law of thermodynamics1×
  • Reversible and irreversible processes4×
  • Entropy4×

Also asked here: calorimetry, expansion, kinetic theory

  • Key points4

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