NEET Physics: Waves – NCERT Masterclass & 100 MCQ Quiz

KINETIC THEORY OF GASES

Complete NCERT Study Notes & 5-Part Mega Quiz for NEET

1. Ideal Gas Equation & Gas Laws

An ideal gas perfectly obeys the gas laws at all temperatures and pressures. Real gases approximate ideal behavior at high temperature and low pressure.

$$PV = nRT = N k_B T$$

Where $R = 8.314 \text{ J/mol K}$ (Universal Gas Constant), $n$ is the number of moles, $N$ is the number of molecules, and $k_B$ is the Boltzmann constant ($1.38 \times 10^{-23} \text{ J/K}$).

• Boyle's Law: $P \propto \frac{1}{V}$ (at constant $T$)
• Charles's Law: $V \propto T$ (at constant $P$)

2. Kinetic Theory Postulates & Pressure

Gases consist of huge numbers of identical, tiny, perfectly elastic point masses in rapid, random motion. The pressure exerted by a gas is due to the continuous elastic collisions of molecules with the walls of the container.

$$P = \frac{1}{3} \rho v_{rms}^2 = \frac{1}{3} \frac{m N}{V} v_{rms}^2$$

3. Kinetic Interpretation of Temperature & Speeds

The absolute temperature of an ideal gas is a direct measure of the average translational kinetic energy of its molecules.

Average Kinetic Energy:
Per Molecule: $E = \frac{3}{2} k_B T$
Per Mole: $E = \frac{3}{2} R T$
(Note: Kinetic energy depends ONLY on absolute temperature, independent of the mass or nature of the gas.)

Molecular Speeds:

• RMS Speed ($v_{rms}$): $\sqrt{\frac{3RT}{M}}$
• Average Speed ($v_{avg}$): $\sqrt{\frac{8RT}{\pi M}}$
• Most Probable Speed ($v_{mp}$): $\sqrt{\frac{2RT}{M}}$

Trick to remember: $v_{rms} > v_{avg} > v_{mp}$

4. Degrees of Freedom & Law of Equipartition of Energy

Degrees of Freedom ($f$): The number of independent ways a dynamic system can move without violating any constraint.

• Monatomic Gas (He, Ne, Ar): $f = 3$
• Diatomic Gas (O₂, N₂, H₂): $f = 5$ (3 translational + 2 rotational)
• Polyatomic non-linear Gas (H₂O, CH₄): $f = 6$ (3 translational + 3 rotational)

Law of Equipartition of Energy: In thermal equilibrium, the total energy is distributed equally amongst all the degrees of freedom, and the energy associated with each molecule per degree of freedom is $\frac{1}{2} k_B T$.

5. Specific Heat Capacity & Mean Free Path

Using equipartition, the molar specific heats are:

$C_v = \frac{f}{2} R$
$C_p = \left(\frac{f}{2} + 1\right) R$
$\gamma = \frac{C_p}{C_v} = 1 + \frac{2}{f}$

Mean Free Path ($\lambda$): The average distance covered by a molecule between two successive collisions.

$$\lambda = \frac{1}{\sqrt{2} \pi n d^2} = \frac{k_B T}{\sqrt{2} \pi d^2 P}$$

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🚀 NEET KINETIC THEORY MEGA QUIZ (100 MCQ)

Solve the 5 parts below to master Gas Laws, RMS Speed, and Thermodynamics Basics.

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