NEET Physics — Kinetic Theory

Chapter Overview & Weightage

Kinetic Theory is one of the easiest scoring chapters in NEET physics. The questions are mostly direct formula plug-ins — rms speed, average kinetic energy, degrees of freedom. The chapter rewards memorisation more than problem-solving skill.

Typical NEET weightage: $1-2$ questions per year.

Year	NEET Qs	Question type
2020	2	rms speed comparison, DOF
2021	1	KE per molecule
2022	2	$C_P/C_V$ ratio
2023	1	Mean free path
2024	2	Speeds at different temperatures

Key Concepts You Must Know

$PV = nRT$ and the link to molecular speeds via $P = \tfrac{1}{3}\rho \langle v^2\rangle$
Three speed expressions and their ratio $\sqrt{3}:\sqrt{8/\pi}:\sqrt{2}$
Average kinetic energy per molecule: $\langle KE\rangle = \tfrac{3}{2}k_B T$
Degrees of freedom and equipartition
$C_V$ , $C_P$ values for monatomic, diatomic, polyatomic
Maxwell-Boltzmann distribution shape (qualitative)

Important Formulas

$v_{\text{rms}} = \sqrt{\frac{3RT}{M}}, \quad v_{\text{avg}} = \sqrt{\frac{8RT}{\pi M}}, \quad v_{\text{mp}} = \sqrt{\frac{2RT}{M}}$

Ratio: $\sqrt{3}:\sqrt{8/\pi}:\sqrt{2} \approx 1.73:1.60:1.41$ .

$\langle KE\rangle = \frac{3}{2}k_B T = \frac{3RT}{2N_A}$

Note: independent of mass! All molecules at the same temperature have the same average translational KE.

Gas type	DOF	$C_V$	$C_P$	$\gamma$
Monatomic	3	$3R/2$	$5R/2$	$5/3$
Diatomic	5	$5R/2$	$7R/2$	$7/5$
Triatomic linear	5	$5R/2$	$7R/2$	$7/5$
Triatomic non-linear	6	$3R$	$4R$	$4/3$

Solved Previous Year Questions

PYQ 1 (NEET 2024)

The ratio of rms speeds of $H_2$ and $O_2$ at the same temperature is approximately:

$v_{\text{rms}} \propto 1/\sqrt{M}$ . So $v_{H_2}/v_{O_2} = \sqrt{M_{O_2}/M_{H_2}} = \sqrt{32/2} = 4$ .

PYQ 2 (NEET 2022)

A diatomic gas has $\gamma = 7/5$ . Find $C_V$ in terms of $R$ .

For diatomic rigid: $\gamma = 7/5 = C_P/C_V$ . With $C_P - C_V = R$ , $C_P = 7R/2$ , $C_V = 5R/2$ .

PYQ 3 (NEET 2021)

What is the average kinetic energy of a gas molecule at $300$ K? ( $k_B = 1.38\times 10^{-23}$ J/K)

$\langle KE\rangle = (3/2) \times 1.38 \times 10^{-23} \times 300 = 6.21 \times 10^{-21}$ J.

Difficulty Distribution

Difficulty	% of NEET Qs	Typical type
Easy	$50\%$	Direct formula plug-in (speed, KE)
Medium	$40\%$	DOF, $\gamma$ identification
Hard	$10\%$	Mean free path, mixed gas problems

Expert Strategy

For NEET, the rms-speed ratio of two gases at the same temperature is $\sqrt{M_2/M_1}$ . Memorise this — it appears every other year.

Average translational KE depends only on temperature, not mass. So $H_2$ and $O_2$ at $300$ K have the same KE per molecule, but different speeds.

For mixed-gas $\gamma$ questions, use $C_V = (n_1 C_{V_1} + n_2 C_{V_2})/(n_1 + n_2)$ then $\gamma = (C_V + R)/C_V$ .

Common Traps

Using temperature in Celsius. Every kinetic-theory formula needs Kelvin. $27^\circ$ C is $300$ K.

Forgetting molar mass units. $R$ in J/(mol·K) requires $M$ in kg/mol. For $M$ in g/mol, use $R = 8.314$ but watch the orders of magnitude.

Saying “all gases at the same temperature have the same rms speed”. The KE is the same, but rms speed depends on $M$ . Heavier molecules move slower.

Counting vibrational DOF for diatomic gases at room temperature. NCERT uses 5 DOF (3 trans + 2 rot) for diatomic at usual temperatures. Vibrations only kick in at high $T$ .