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NTA Abhyas 2020
Exam
NTA Abhyas
Year
2020
Subject
Physics
Chapter
Kinetic Theory of Gases

NTA Abhyas 2020 · Physics · Kinetic Theory of Gases

The temperature of an ideal gas is increased from 100K to 400K . If...

The temperature of an ideal gas is increased from 100K100K to 400K400K. If the rr ms speed of the gas molecule is VV at 100K100K , then at 400K400K it becomes

Options

  1. A2V2V
  2. B4V4V
  3. C0.5V0.5V
  4. DVV

Correct answer

A. 2V2V

Step-by-step solution

∵rms∵ rms speed of molecule Vrms∝T{V}_{rms} ∝ \sqrt{T}

for T=100KT = 100K

(Vrms)1∝100{\left({V}_{rms}\right)}_{1} ∝ \sqrt{100}

For T=400KT = 400K

(Vrms)2∝400{\left({V}_{rms}\right)}_{2} ∝ \sqrt{400}

therefore, (Vrms)1(Vrms)2=100400\dfrac{{\left({V}_{rms}\right)}_{1}}{{\left({V}_{rms}\right)}_{2}} = \dfrac{\sqrt{100}}{\sqrt{400}}

or V(Vrms)2=12\dfrac{V}{{\left({V}_{rms}\right)}_{2}} = \dfrac{1}{2}

or (Vrms)2=2V{\left({V}_{rms}\right)}_{2} = 2V
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