Quantrex Quantrex AcademyJEE · NEET · NDA PYQs with solutions Open app
JEE Main 202311 AprilEvening Shift
Exam
JEE Main
Year
2023
Date
11 April
Shift
Evening Shift
Subject
Physics
Chapter
Kinetic Theory of Gases

JEE Main 2023 · 11 April · Evening Shift · Physics · Kinetic Theory of Gases

The root mean square speed of molecules of nitrogen gas at 27 ° C...

The root mean square speed of molecules of nitrogen gas at 27°C27 ° C is approximately: (Given mass of a nitrogen molecule =4.6×10−26kg= 4 . 6 \times {10}^{- 26}kg and take Boltzmann constant kB=1.4×10−23JK−1{k}_{B} = 1 . 4 \times {10}^{- 23}J{K}^{- 1} )

Options

  1. A27.4ms−127 . 4m{s}^{- 1}
  2. B91ms−191m{s}^{- 1}
  3. C1260ms−11260m{s}^{- 1}
  4. D523ms−1523m{s}^{- 1}

Correct answer

D. 523ms−1523m{s}^{- 1}

Step-by-step solution

The RMS value of a gas is given by

vrms=3RTM=3kBTm{v}_{rms} = \sqrt{\dfrac{3RT}{M}} = \sqrt{\dfrac{3{k}_{B}T}{m}}

Substituting the given values,

vrms=3×1.4×10−23×3004.6×10−26{v}_{rms} = \sqrt{\dfrac{3 \times 1 . 4 \times {10}^{- 23} \times 300}{4 . 6 \times {10}^{- 26}}}
≈523ms−1\approx 523m{s}^{- 1}

Practice Kinetic Theory of Gases on Quantrex Academy →

More from Kinetic Theory of Gases

If 2 mole of an ideal monoatomic gas at temperature T , is mixed with 6 mole of another… JEE Main 2026Given below are two statements: one is labelled as Assertion A and the other is labelled… JEE Main 2026Given below are two statements: one is labelled as Assertion A and the other is labelled… JEE Main 2026One gas of n_1 mole of molecules at temperature T_1 , volume V_1 , and pressure P_1 , and… JEE Main 2026A mixture of carbon dioxide and oxygen has volume 8310 cm ^3 , temperature 300 K… JEE Main 2026The mean free path of a molecule of diameter 5 × 10^ -10 ~m at the temperature 41^ ∘ C… JEE Main 2026A gas of certain mass filled in a closed cylinder at a pressure of 3.23 kPa has… JEE Main 2026Consider two boxes containing ideal gases A and B such that their temperatures, pressures… JEE Main 2026 Full Kinetic Theory of Gases list All JEE Main PYQs