IIT JEE Test Series — Practice smarter, perform stronger.

Kinetic Theory of Gases formulas

Master Kinetic Theory of Gases through 22 JEE Advanced-level formulas, systematically structured with every variable spelled out. Revise concept-wise, identify the areas where you need improvement, and focus your preparation with greater precision.

Practise these formulas Know more about IIT JEE

Back to Formula Book

Kinetic Theory of Gases, every formula

22 formulas, typeset and free. Print it, or keep it open beside your practice.

Ideal gas law
$P V = n R T$
Q1MCQIdeal gas
The ideal gas law is:
- A
  $PV=nRT$
- B
  $PV=\dfrac{nR}{T}$
- C
  $P=nRTV$
- D
  $PV=RT$
Ideal gas (molecules)
$P V = N k_{B} T$
Q1MCQGas (molecules)
In terms of molecules, the ideal gas law is:
- A
  $PV=Nk_BT$
- B
  $PV=NRT$
- C
  $P=Nk_BT$
- D
  $PV=\dfrac{N}{k_BT}$
Pressure (kinetic)
$P = \frac{1}{3} ρ \overline{v^{2}} = \frac{1}{3} \frac{m N}{V} \overline{v^{2}}$
Q1MCQKinetic pressure
The pressure of a gas from kinetic theory is:
- A
  $\tfrac13\rho\,\overline{v^{2}}$
- B
  $\rho\,\overline{v^{2}}$
- C
  $\tfrac12\rho\,\overline{v^{2}}$
- D
  $\tfrac23\rho\,\overline{v^{2}}$
RMS speed
$v_{r m s} = \frac{3 R T}{M} = \frac{3 k _{B} T}{m}$
Q1MCQRMS speed
The rms speed of gas molecules is:
- A
  $\sqrt{\dfrac{3RT}{M}}$
- B
  $\sqrt{\dfrac{2RT}{M}}$
- C
  $\sqrt{\dfrac{8RT}{\pi M}}$
- D
  $\sqrt{\dfrac{RT}{M}}$
Average speed
$v_{a v g} = \frac{8 R T}{π M}$
Q1MCQAverage speed
The average speed of gas molecules is:
- A
  $\sqrt{\dfrac{8RT}{\pi M}}$
- B
  $\sqrt{\dfrac{3RT}{M}}$
- C
  $\sqrt{\dfrac{2RT}{M}}$
- D
  $\sqrt{\dfrac{RT}{M}}$
Most probable speed
$v_{m p} = \frac{2 R T}{M}$
Q1MCQMost probable speed
The most probable speed is:
- A
  $\sqrt{\dfrac{2RT}{M}}$
- B
  $\sqrt{\dfrac{3RT}{M}}$
- C
  $\sqrt{\dfrac{8RT}{\pi M}}$
- D
  $\sqrt{\dfrac{RT}{M}}$
Speed ratio
$v_{m p} : v_{a v g} : v_{r m s} = 1 : 1.13 : 1.22$
Q1MCQSpeed order
The correct order of molecular speeds is:
- A
  $v_{mp}<v_{avg}<v_{rms}$
- B
  $v_{rms}<v_{avg}<v_{mp}$
- C
  all equal
- D
  $v_{avg}<v_{mp}<v_{rms}$
Average KE per molecule
$\overline{K E} = \frac{3}{2} k_{B} T$
Q1MCQKE per molecule
The average kinetic energy per molecule is:
- A
  $\tfrac32 k_BT$
- B
  $\tfrac12 k_BT$
- C
  $\tfrac32 RT$
- D
  $k_BT$
Average KE per mole
$K E = \frac{3}{2} R T$
Q1MCQKE per mole
The average kinetic energy per mole is:
- A
  $\tfrac32 RT$
- B
  $\tfrac32 k_BT$
- C
  $\tfrac12 RT$
- D
  $RT$
Energy per degree of freedom
$\frac{1}{2} k_{B} T per degree of freedom$
Q1MCQEquipartition
The energy per degree of freedom per molecule is:
- A
  $\tfrac12 k_BT$
- B
  $\tfrac32 k_BT$
- C
  $k_BT$
- D
  $\tfrac12 RT$
Internal energy (f d.o.f.)
$U = \frac{f}{2} n R T$
Q1MCQInternal energy
The internal energy of $n$ moles with $f$ degrees of freedom is:
- A
  $\dfrac{f}{2}nRT$
- B
  $\dfrac{3}{2}nRT$
- C
  $fnRT$
- D
  $\dfrac{n}{2}RT$
Degrees of freedom
$f = 3 (mono), 5 (dia), 6 (polyatomic)$
Cv and Cp
$C_{v} = \frac{f}{2} R, C_{p} = (\frac{f}{2} + 1) R$
Q1MCQCv
For a gas with $f$ degrees of freedom, $C_v$ is:
- A
  $\dfrac{f}{2}R$
- B
  $\dfrac{f}{2}R+R$
- C
  $fR$
- D
  $\dfrac{R}{f}$
Mayer's relation
$C_{p} - C_{v} = R$
Q1MCQMayer's relation
For an ideal gas, $C_p-C_v$ equals:
- A
  $R$
- B
  $\dfrac{R}{2}$
- C
  $2R$
- D
  $0$
Adiabatic exponent
$γ = \frac{C _{p}}{C _{v}} = 1 + \frac{2}{f}$
Q1MCQGamma
The ratio $\gamma=\dfrac{C_p}{C_v}$ equals:
- A
  $1+\dfrac{2}{f}$
- B
  $1-\dfrac{2}{f}$
- C
  $\dfrac{f}{2}$
- D
  $\dfrac{2}{f}$
Mean free path
$λ = \frac{1}{2 π d ^{2} n}$
Q1MCQMean free path
The mean free path of a gas molecule is:
- A
  $\dfrac{1}{\sqrt2\,\pi d^{2}n}$
- B
  $\sqrt2\,\pi d^{2}n$
- C
  $\dfrac{1}{\pi d^{2}n}$
- D
  $\dfrac{n}{\pi d^{2}}$
Boltzmann constant
$k_{B} = \frac{R}{N _{A}} = 1.38 \times 1 0^{- 23} J/K$
Q1MCQBoltzmann constant
The Boltzmann constant equals:
- A
  $\dfrac{R}{N_A}$
- B
  $R N_A$
- C
  $\dfrac{N_A}{R}$
- D
  $R$
Avogadro's law
$equal volumes, same T,P \Rightarrow equal molecules$
Q1MCQAvogadro's law
Equal volumes of gases at the same T and P contain:
- A
  equal numbers of molecules
- B
  equal masses
- C
  equal densities
- D
  equal speeds
Dalton's law
$P = P_{1} + P_{2} + \dots$
Q1MCQDalton's law
The total pressure of a mixture of non-reacting gases is:
- A
  the sum of partial pressures
- B
  the average of partial pressures
- C
  the product of pressures
- D
  the largest partial pressure
Gas density
$ρ = \frac{P M}{R T}$
Q1MCQGas density
The density of an ideal gas is:
- A
  $\dfrac{PM}{RT}$
- B
  $\dfrac{RT}{PM}$
- C
  $\dfrac{PMR}{T}$
- D
  $PMRT$
vrms temperature dependence
$v_{r m s} \propto T$
Q1MCQvrms vs T
The rms speed of a gas varies with temperature as:
- A
  $\sqrt{T}$
- B
  $T$
- C
  $T^{2}$
- D
  $\dfrac{1}{T}$
vrms mass dependence
$v_{r m s} \propto \frac{1}{M}$
Q1MCQvrms vs M
For a fixed temperature, the rms speed varies with molar mass as:
- A
  $\dfrac{1}{\sqrt{M}}$
- B
  $\sqrt{M}$
- C
  $M$
- D
  $\dfrac{1}{M}$

Other ways to revise this chapter

Master this chapter with similar other learning materials.

Preparing students for India’s top institutes

Our students are currently into top technological and medical institutes of India.

IIT Bombay
IIT Delhi
IIT Madras
IIT Kanpur
IIT Kharagpur
IIT Roorkee
IIT Guwahati
IIT BHU Varanasi
AIIMS Delhi
NIT Tiruchirappalli
NIT Rourkela
IIT Bombay
IIT Delhi
IIT Madras
IIT Kanpur
IIT Kharagpur
IIT Roorkee
IIT Guwahati
IIT BHU Varanasi
AIIMS Delhi
NIT Tiruchirappalli
NIT Rourkela

Join QuestPix, Today!

Get notified first, with exam & curriculum updates, course & test series launch offers, motivation & success stories and free learning resources recommended by toppers.

Kinetic Theory of Gases formulas

Kinetic Theory of Gases, every formula

Ideal gas law

Ideal gas (molecules)

Pressure (kinetic)

RMS speed

Average speed

Most probable speed

Speed ratio

Average KE per molecule

Average KE per mole

Energy per degree of freedom

Internal energy (f d.o.f.)

Degrees of freedom

Cv and Cp

Mayer's relation

Adiabatic exponent

Mean free path

Boltzmann constant

Avogadro's law

Dalton's law

Gas density

vrms temperature dependence

vrms mass dependence

More JEE Advanced Physics formula sheets

Other ways to revise this chapter

Preparing students for India’s top institutes

Join QuestPix, Today!