AimMent
Exam level2 past questions

RMS speed and temperature dependence

The root mean square (rms) speed of gas molecules depends on temperature and molar mass, and is a key measure of molecular motion in gases.

Why this shows up in the exam

NEET often asks you to calculate or compare rms speeds under different conditions using kinetic theory formulas.

How NEET tests this

Numerical · 2 QsMatch the columns

Learn the idea

RMS speed of a gas molecule is √(3RT/M); the key insight is that temperature appears under a square‑root while mass sits in the denominator, so a hotter or lighter gas moves faster.

🧠 Memory hook: RMS = ‘Racing Mouse Speed’ – the mouse runs faster on a hotter track (√T) but slows if it carries a heavier backpack (÷√M).

Get this one clearly and it pays off every single time it shows up in the paper. 🎯

Formulas & facts to keep ready

  • vrms = √(3RT/M)
  • Average kinetic energy of one molecule = 3/2 kB T
  • Pressure P = 1/3 n m vrms² (n = number density)
  • Internal energy of 1 mol diatomic gas = 5/2 RT
  • Temperature must be in Kelvin
  • M is the molar mass (kg mol⁻¹)

How to approach it

  1. 1Convert every temperature to Kelvin
  2. 2If M is unchanged, use vrms₂ = vrms₁·√(T₂/T₁)
  3. 3When pressure also changes, find new number density from PV = nRT and substitute in P = 1/3 n m vrms²
  4. 4Choose the formula that matches the quantity asked (speed, pressure, kinetic energy, internal energy)

Worked example — watch it click

Match Column-I and Column-II and choose the correct match from the given choices. Column-I (A) Root mean square speed of gas molecules (B) Pressure exerted by ideal gas (C) Average kinetic energy of a molecule (D) Total internal energy of 1 mole of a diatomic gas Column-II (P) 1/3 nmv² (Q) √(3RT/M) (R) 5/2 RT (S) 3/2 kBT

  • A)(A)-(R), (B)-(Q), (C)-(P), (D)-(S)
  • B)(A)-(R), (B)-(P), (C)-(S), (D)-(Q)
  • C)(A)-(Q), (B)-(R), (C)-(S), (D)-(P)
  • ✅(A)-(Q), (B)-(P), (C)-(S), (D)-(R)

The concept behind this problem

The worked example forces you to pair each physical quantity with its exact kinetic‑theory expression, testing whether you recognise the √(3RT/M) form for rms speed, the 1/3 n m vrms² form for pressure, 3/2 kB T for molecular kinetic energy, and 5/2 RT for the internal energy of a diatomic mole.

Step by step

  1. 1(A) Root mean square speed = √(3RT/M) matches (Q).
  2. 2(B) Pressure exerted by ideal gas: from kinetic theory, P = (1/3)nmv̄² where n is number density, matches (P).
  3. 3(C) Average kinetic energy of a molecule = (3/2)kᵦT matches (S).
  4. 4(D) Total internal energy of 1 mole of diatomic gas = (5/2)RT (3 translational + 2 rotational degrees of freedom) matches (R).

Watch out

Students often swap the pressure expression (1/3 n m vrms²) with the rms‑speed formula (√(3RT/M)).

Common slip-ups that cost marks

  • •Using °C directly instead of Kelvin
  • •Confusing rms speed with average or most‑probable speed
  • •Leaving out the factor 1/3 in the pressure expression or swapping it with the rms‑speed formula

🌟 That's the whole idea — you've got this. Try the practice set below; every question you attempt makes it stick a little harder.

Practise it

These are real questions from past NEET papers that test this exact idea.

Question 1 of 2NEET 2016

The molecules of a given mass of a gas have rms velocity of 200 m s at 27° C and 1.0 × 10⁵ N m⁻² pressure. When the temperature and pressure of the gas are, respectively, 127° C and 0.05 × 10⁵ N m⁻², the rms velocity of its molecules in m s⁻¹ is:

Push further

More challenging

2 harder questions built from the past papers above — a step up in difficulty, with distractors designed so you can't get there by elimination. Written and checked by our reviewers, not from a real paper.

Question 1 of 2

At what temperature will the RMS velocity of hydrogen molecules be twice its value at 27°C?

More from Kinetic Theory of Gases