Kinetic Theory of Gases formulas

Every formula JEE Advanced expects you to know for Kinetic Theory of Gases, with the variables spelled out. Free, no sign-up. Read it before a mock, not during one.

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Formulas: 22
Subject: Physics
Exam: JEE Advanced
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Kinetic Theory of Gases, every formula

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

Ideal gas law
$P V = n R T$
Ideal gas (molecules)
$P V = N k_{B} T$
Pressure (kinetic)
$P = \frac{1}{3} ρ \overline{v^{2}} = \frac{1}{3} \frac{m N}{V} \overline{v^{2}}$
RMS speed
$v_{r m s} = \frac{3 R T}{M} = \frac{3 k _{B} T}{m}$
Average speed
$v_{a v g} = \frac{8 R T}{π M}$
Most probable speed
$v_{m p} = \frac{2 R T}{M}$
Speed ratio
$v_{m p} : v_{a v g} : v_{r m s} = 1 : 1.13 : 1.22$
Average KE per molecule
$\overline{K E} = \frac{3}{2} k_{B} T$
Average KE per mole
$K E = \frac{3}{2} R T$
Energy per degree of freedom
$\frac{1}{2} k_{B} T per degree of freedom$
Internal energy (f d.o.f.)
$U = \frac{f}{2} n R T$
Degrees of freedom
$f = 3 (mono), 5 (dia), 6 (polyatomic)$
Cv and Cp
$C_{v} = \frac{f}{2} R, C_{p} = (\frac{f}{2} + 1) R$
Mayer's relation
$C_{p} - C_{v} = R$
Adiabatic exponent
$γ = \frac{C _{p}}{C _{v}} = 1 + \frac{2}{f}$
Mean free path
$λ = \frac{1}{2 π d ^{2} n}$
Boltzmann constant
$k_{B} = \frac{R}{N _{A}} = 1.38 \times 1 0^{- 23} J/K$
Avogadro's law
$equal volumes, same T,P \Rightarrow equal molecules$
Dalton's law
$P = P_{1} + P_{2} + \dots$
Gas density
$ρ = \frac{P M}{R T}$
vrms temperature dependence
$v_{r m s} \propto T$
vrms mass dependence
$v_{r m s} \propto \frac{1}{M}$

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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

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