PREPWISER.
Practise online

Kinetic Theory of Gases revision notes

Every idea in the Kinetic Theory of Gases chapter for JEE Main, with the usual mistakes and the fast methods. Topic 1 is open to everyone; sign in free to read all 26 and download the PDF.

Sign in to read all 26Download PDF

Read the first part free. Sign in free with Google to read the rest and download the PDF: 9 A4 pages.9 A4 pages, ready to print.

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.

Ideal gas equation and gas laws

Ideal gas equation
11× asked, last 2024
PV=nRT=NkT,n=mM=NNAPV = nRT = NkT,\qquad n=\frac{m}{M}=\frac{N}{N_A}
TT in kelvin, PP in Pa, VV in m³. R=8.314R=8.314 J mol⁻¹ K⁻¹. Also P=nvkTP=n_vkT with nvn_v molecules per m³.
  • Energy per molecule given: kT=2Eˉ/3kT=2\bar E/3 from Eˉ=3kT/2\bar E=3kT/2, then N=PV/kTN=PV/kT. Molecules per volume given: P=nvkTP=n_vkT, so T=P/nvkT=P/n_vk.
  • Molecules that break up change the count: if a fraction xx of diatomic molecules dissociates, n→n(1+x)n\to n(1+x). Recount the moles before using PV=nRTPV=nRT.
  • Not atomic masses for H₂, O₂, N₂. Use molecular masses 2, 32 and 28 g/mol, because these gases exist as molecules; atomic masses double the number of moles.
  • Not mixed units. Convert atm to Pa (×1.013×105\times1.013\times10^5) and L or cm³ to m³ first, because RR and kk are SI values. Wrong options are often a power of ten off.
Density form
1× asked, last 2024
P=ρRTM,PρT=constantP=\frac{\rho RT}{M},\qquad \frac{P}{\rho T}=\text{constant}
Fixed gas. A PP–TT line at fixed density has slope ρR/M\rho R/M: the steeper line is the denser gas.
Gas laws
9× asked, last 2025
PV=const  (T),VT=const  (P),PT=const  (V)PV=\text{const}\;(T),\qquad \frac{V}{T}=\text{const}\;(P),\qquad \frac{P}{T}=\text{const}\;(V)
Boyle, Charles, Gay-Lussac; fixed amount of gas. TT always in kelvin, though a 1 °C change equals a 1 K change.
tt (°C)VV−273-273P1P_1P2=2P1P_2=2P_10 K
Isobars extrapolate to zero volume at −273-273 °C (0 K); the steeper line is the lower pressure
  • Graphs: VV–TT at fixed PP is a line through 0 K with slope nR/PnR/P, so a steeper line means lower pressure. PP–TT lines at fixed VV all meet at −273∘-273^\circC.
  • Not Celsius in a ratio. P∝TP\propto T holds only in kelvin. Convert, scale, then convert back by subtracting 273; heating gas in a rigid closed vessel always raises its pressure.
  • Quick method. Small changes: ΔP/P=ΔT/T\Delta P/P=\Delta T/T at fixed VV. For any law PaVbTcP^aV^bT^c = const, fractional changes add with these powers: a ΔP/P+b ΔV/V+c ΔT/T=0a\,\Delta P/P+b\,\Delta V/V+c\,\Delta T/T=0.
Volume expansion coefficient
1× asked, last 2023
γV=1VdVdT,V∝T x  ⇒  γV=xT\gamma_V=\frac{1}{V}\frac{dV}{dT},\qquad V\propto T^{\,x}\;\Rightarrow\;\gamma_V=\frac{x}{T}
Ideal gas at constant PP: γV=1/T\gamma_V=1/T. For a law like PTaPT^a = const, first turn it into V∝TxV\propto T^x using PV=nRTPV=nRT.
Mixtures: Dalton's law
6× asked, last 2024
P=∑Pi=(n1+n2+… )RTV,Pi=niRTVP=\sum P_i=\frac{(n_1+n_2+\dots)RT}{V},\qquad P_i=\frac{n_iRT}{V}
Non-reacting ideal gases sharing volume VV at one TT. Only the total moles matter, not which gas.
  • Not masses in PV=nRTPV=nRT. Add moles mi/Mim_i/M_i, because every mole pushes equally whatever the gas. Equal masses in equal vessels: the lighter gas gives the higher pressure.
  • Quick method. Two unknown amounts in a mixture: PV=nRTPV=nRT gives n1+n2n_1+n_2 and the total mass gives n1M1+n2M2n_1M_1+n_2M_2. Solve both, then give the ratio in the order asked.
Connected vessels and leaks
2× asked, last 2025
∑iPiViTi=Pf∑iViTf,i\sum_i\frac{P_iV_i}{T_i}=P_f\sum_i\frac{V_i}{T_{f,i}}
Total moles conserved; final PfP_f is common, vessel ii ends at Tf,iT_{f,i}. One final TT: right side is Pf(V1+V2)/TfP_f(V_1+V_2)/T_f.
  • Partition removed at one temperature: P=(P1V1+P2V2)/(V1+V2)P=(P_1V_1+P_2V_2)/(V_1+V_2). Gas leaking from a rigid vessel: moles ∝P/T\propto P/T, so the fraction left is (P2/T2)/(P1/T1)(P_2/T_2)/(P_1/T_1).
Work on compressing a gas
Won gas=−∫V1V2P dV,Wiso=nRTln⁡V1V2W_{\text{on gas}}=-\int_{V_1}^{V_2}P\,dV,\qquad W_{\text{iso}}=nRT\ln\frac{V_1}{V_2}
Positive when compressed (V2<V1V_2<V_1). Isothermal, adiabatic and cyclic work: see the Thermodynamics sheet.

Practise Kinetic Theory of Gases questions as you read. Free, and you can start without signing up.

Practise Kinetic Theory of Gases

19 more concepts in 6 topics

Kinetic theory: pressure and temperature, Molecular speeds, Degrees of freedom and equipartition, Specific heats and gas mixtures and Mean free path and collisions, plus ideas from thermodynamics. Read the first part free. Sign in free with Google to read the rest and download the PDF.

Sign in to read the restYou come straight back to this spot.Download the PDF

Kinetic theory: pressure and temperature

  • Assumptions of kinetic theory1×
  • Pressure of an ideal gas5×
  • Kinetic interpretation of temperature16×
  • Avogadro's number and Boltzmann constant3×
  • Real gases1×

Molecular speeds

  • RMS speed23×
  • Average and most probable speeds7×
  • Ratio of the three speeds4×
  • Speed of sound and rms speed1×

Degrees of freedom and equipartition

  • Degrees of freedom15×
  • Law of equipartition7×
  • Internal energy of an ideal gas11×
  • Moving container stopped suddenly2×

Specific heats and gas mixtures

  • Molar specific heats11×
  • Ratio of specific heats12×
  • Specific heats of a gas mixture7×
  • Mixing gases: final temperature2×

Mean free path and collisions

  • Mean free path8×
  • Collision frequency and mean free time8×

Also asked here: thermodynamics

  • Key points1

Practise Kinetic Theory of Gases next

About 130 past JEE Main questions from this chapter, with instant answer checking and step-by-step solutions where available. Free, and you can start without signing up.

Practise Kinetic Theory of Gases

Also free on PrepWiser

Spotted a mistake? Write to support@prepwiser.in and we will fix it in the next version.

Version 1, October 2026. Free to share for study, as it is. Please don't sell it or remove the PrepWiser name.

PractiseSign in to read all 26Download PDF
Free with Google, takes a few seconds9 pages, free