Q.26 Physics ⭐ 360° Option Elimination Active

NEET 2021 Physics Question 26 Solution

Topic: Kinetic Theory · Official NTA Booklet Code M1

Question

Match Column - I and Column - II and choose the correct match from the given choices. Column - I Column - II (A) Root mean square (P) 1 nm v speed of gas molecules (B) Pressure exerted (Q) 3 RT by ideal gas (C) Average kinetic energy (R) 5 RT of a molecule (D) Total internal energy (S) 3 k T of 1 mole of a diatomic gas

(1)(A) - (R), (B) - (P), (C) - (S), (D) - (Q)
(2)(A) - (Q), (B) - (R), (C) - (S), (D) - (P)
(3)(A) - (Q), (B) - (P), (C) - (S), (D) - (R)
(4)(A) - (R), (B) - (Q), (C) - (P), (D) - (S)

✓

Verified Against NTA Final Answer Key

Option (3) : (A) - (Q), (B) - (P), (C) - (S), (D) - (R)

📚 Kinetic Theory Easy

📋 Given Parameters & Problem Setup

Column I (A) Root mean square speed, (B) Pressure exerted by ideal gas, (C) Average KE of a molecule, (D) Total internal energy of 1 mole of diatomic gas

Column II (P) 1/3 n m v_bar^2, (Q) \sqrt{3RT / M}, (R) 5/2 RT, (S) 3/2 k_B T

⚡

The 30-Second Exam Hall Shortcut: ⚡ Kinetic Theory Master Matcher

⏱️ Save ~25 seconds

Match standard NCERT kinetic theory relations: RMS speed $v_{\text{rms}} = \sqrt{\frac{3RT}{M}}$ (Q); Pressure $P = \frac{1}{3} n m \bar{v}^2$ (P); Average KE of one molecule $= \frac{3}{2} k_B T$ (S); Internal energy of 1 mole of diatomic gas ( $f=5$ ) $= \frac{5}{2} RT$ (R)! Match Option (3)!

1 RMS speed of gas molecules:

v_{\text{rms}} = \sqrt{\frac{3RT}{M}} \implies (A)-(Q)

2 Pressure of ideal gas:

P = \frac{1}{3} n m \bar{v}^2 \implies (B)-(P)

3 Translational KE per single molecule:

\bar{E} = \frac{3}{2} k_B T \implies (C)-(S)

4 Total internal energy for 1 mole of diatomic gas (

f = 5

degrees of freedom):

U = \frac{f}{2} RT = \frac{5}{2} RT \implies (D)-(R)

5 Match combination: (A)-(Q), (B)-(P), (C)-(S), (D)-(R) -> Option (3).

🛡️

Why You Can 100% Trust This Shortcut: Canonical Maxwell-Boltzmann kinetic theory of ideal gases and equipartition of energy theorem.

📐

Step-by-Step Rigorous Workflow & Mathematical Proof

Step 1

Formula for RMS Speed of Gas Molecules (A)

From kinetic theory of gases, the root mean square speed is directly proportional to the square root of absolute temperature:

v_{\text{rms}} = \sqrt{\frac{3RT}{M}} \implies \mathbf{(A)-(Q)}

Step 2

Formula for Pressure Exerted by an Ideal Gas (B)

Derived by considering rate of change of momentum of gas molecules bombarding container walls, where $n$ is number density, $m$ is molecular mass, and $\bar{v}^2$ is mean square speed:

P = \frac{1}{3} n m \bar{v}^2 \implies \mathbf{(B)-(P)}

Step 3

Formula for Average Kinetic Energy of a Molecule (C)

By the equipartition of energy theorem, each translational degree of freedom contributes $\frac{1}{2} k_B T$ . For 3 translational degrees of freedom of a single molecule:

E_{\text{avg}} = 3 \times \left(\frac{1}{2} k_B T\right) = \frac{3}{2} k_B T \implies \mathbf{(C)-(S)}

Step 4

Formula for Total Internal Energy of 1 Mole of Diatomic Gas (D)

A rigid diatomic gas has 5 degrees of freedom (3 translational + 2 rotational). For 1 mole ( $n = 1$ ), the internal energy is:

U = \frac{f}{2} n R T = \frac{5}{2} (1) R T = \frac{5}{2} R T \implies \mathbf{(D)-(R)}

⭐

360° Option Elimination Engine Key Feature

Diagnose every choice: Know exactly why the right option works and why distractors fail.

4-Option Deep Scan

1 1

✗ Incorrect

Verdict & Scientific Reason:

Mismatches RMS speed with internal energy $\frac{5}{2}RT$ .

⚠️

Student Fallacy (Why candidates pick this trap): Swapping (A) and (D).

2 2

✗ Incorrect

Verdict & Scientific Reason:

Mismatches pressure with internal energy.

⚠️

Student Fallacy (Why candidates pick this trap): Swapping (B) and (D).

3 3

✓ 100% Correct

Verdict & Scientific Reason:

Exact 1-to-1 match with all four textbook kinetic theory relations.

💡

Why this is airtight: None; textbook verbatim match.

4 4

✗ Incorrect

Verdict & Scientific Reason:

Scrambles multiple associations.

⚠️

Student Fallacy (Why candidates pick this trap): Random matching.

⚠️

NTA Trap Alert: Molar Energy (R) vs. Molecular Energy (k_B) Trap

Students frequently mix up molecular kinetic energy (which uses Boltzmann's constant $k_B$ ) with molar internal energy (which uses the universal gas constant $R$ ).

🛡️ How to avoid the -1 mark: Molecule = uses

k_B

(Option S). Mole of gas = uses

R

(Option R).

📖

Core NEET Syllabus Standard

NCERT Physics · Kinetic Theory Standard Benchmark

Core Scientific Principle Tested:

"Pressure is $P = \frac{1}{3}nm\bar{v}^2$ ; RMS speed is $\sqrt{3RT/M}$ ; average molecular KE is $\frac{3}{2}k_BT$ ; internal energy of diatomic gas is $\frac{5}{2}RT$ ."

Syllabus Focus: Pressure of an Ideal Gas, Kinetic Interpretation of Temperature, and Law of Equipartition of Energy

✓ Core NEET UG Syllabus Anchor Syllabus & Academic Standards ↗

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NEET 2021 Physics Question 26 Solution

Question

The 30-Second Exam Hall Shortcut: ⚡ Kinetic Theory Master Matcher

Step-by-Step Rigorous Workflow & Mathematical Proof

Formula for RMS Speed of Gas Molecules (A)

Formula for Pressure Exerted by an Ideal Gas (B)

Formula for Average Kinetic Energy of a Molecule (C)

Formula for Total Internal Energy of 1 Mole of Diatomic Gas (D)

360° Option Elimination Engine Key Feature

NTA Trap Alert: Molar Energy (R) vs. Molecular Energy (k_B) Trap

Core NEET Syllabus Standard

Ready to attempt under real exam pressure?

🔗 Related Questions — Kinetic Theory

Mean Free Path Dependency on Molecular Diameter and Number Density

Gas Withdrawal, Gauge Pressure vs. Absolute Pressure & Mass Loss

Comparison of Pressures from T-V Curves

RMS Speed Dependence on Temperature

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