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Kinetic Theory of Gases formula sheet

Every formula in the Kinetic Theory of Gases chapter for JEE Main, with one line on when it applies. Topic 1 is open to everyone; sign in free to read all 25 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 formula, and "last" is the latest year one appeared. ★ marks formulas 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 mM=\frac N{N_A}
SI units, TT in K; R=8.314R=8.314 J mol−1^{-1}K−1^{-1}. Also P=nvkTP=n_vkT. H2\mathrm{H_2}, O2\mathrm{O_2}, N2\mathrm{N_2}: molecular masses.
Density form
1× asked, last 2024
P=ρRTM,PρT=constantP=\frac{\rho RT}M,\qquad \frac P{\rho T}=\text{constant}
Fixed gas. PP–TT line at fixed ρ\rho: slope ρR/M\rho R/M.
Gas laws
9× asked, last 2025
PV=const (T),VT=const (P),PT=const (V)PV=\text{const}\ (T),\qquad \frac VT=\text{const}\ (P),\qquad \frac PT=\text{const}\ (V)
Kelvin always. VV–TT slope nR/PnR/P: steeper = lower pressure.
Small changes
PaVbTc=const ⇒ aΔPP+bΔVV+cΔTT=0P^aV^bT^c=\text{const}\ \Rightarrow\ a\frac{\Delta P}P+b\frac{\Delta V}V+c\frac{\Delta T}T=0
E.g. fixed VV: ΔP/P=ΔT/T\Delta P/P=\Delta T/T.
Volume expansion coefficient
1× asked, last 2023
γV=1VdVdT,V∝Tx ⇒ γV=xT\gamma_V=\frac1V\frac{dV}{dT},\qquad V\propto T^x\ \Rightarrow\ \gamma_V=\frac xT
Ideal gas at constant PP: γV=1/T\gamma_V=1/T.
Dalton's law
6× asked, last 2024
P=∑Pi=(n1+n2+… )RTVP=\sum P_i=\frac{(n_1+n_2+\dots)RT}V
Add moles mi/Mim_i/M_i, not masses. Equal masses: the lighter gas gives more pressure.
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}}
Moles conserved. Leak from a rigid vessel: fraction left =(P2/T2)/(P1/T1)=(P_2/T_2)/(P_1/T_1).

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Practise Kinetic Theory of Gases

18 more formulas in 5 topics

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

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Kinetic theory: pressure and temperature

  • Pressure of an ideal gas5×
  • Temperature and kinetic energy16×
  • Avogadro and Boltzmann3×
  • Real gases

Molecular speeds

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

Degrees of freedom and equipartition

  • Degrees of freedom15×
  • Law of equipartition7×
  • Internal energy11×
  • Moving container stopped2×

Specific heats and gas mixtures

  • Molar specific heats11×
  • Ratio of specific heats12×
  • Gas mixture7×
  • Mixing gases: final temperature2×

Mean free path and collisions

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

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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.

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